Usage and alternative words
A simple answer to this one: no, there is no word for pescetarians that is more commonly used or understood than pescetarian (or pescatarian, if you prefer that spelling).
It is not a concept that has been spoken about commonly for very long, and pescetarian is, to my knowledge, the only word for it that has any practical currency at all. It is not overly common, but it is also not limited to “strict circles”. It is not uncommon for average people (with no special dietary habits) to know at least more or less what a pescetarian is.
A perhaps more transparent alternative is pesco-vegetarian, which more overtly marks the connection between pescetarianism and vegetarianism. It may be easier for people who do not know what pescetarianism is to grasp the meaning of pesco-vegetarian, but it is not in as common use as pescetarian.
At least equally common as pescetarian, though, is misuse of the term vegetarian. By any commonly accepted definition, a vegetarian does not eat any kind of meat, including poultry and fish; but quite a few people do not consider fish and/or poultry ‘meat’ and thus do not distinguish vegetarians and pescetarians (and often not vegans, either).1 It is my personal experience, however, that the percentage of people who use vegetarian to refer to pescetarians is decreasing. Ten or 15 years ago, nearly everyone thought people who only ate fish were vegetarian; nowadays, the split between those who call it vegetarian and those who call it pescetarian is more like 50/50. (Excluding of course the ones who do not know that there is a term for either thing, which these days is a definite minority.)
Your best bet is to simply get used to pescetarian, even if you do think it is awkward, because there is no better alternative. Alternatively, if you want to make sure you’re understood and don’t care it’s a bit longer, explain: “I tend towards vegetarianism, but I do eat fish as well” or something like that.
Origin of the word
The established theory
As both Merriam-Webster, Wikipedia, and the OED mention, the formation of the word is not quite clear. The second element, -tarian, is clear enough: it originated in vegetarian, whence it spread to other types of ‘dietary lifestyles’. Vegetarian is itself a more or less ad-hoc blend of vegetable (or possibly vegetation) and the weakly productive suffix -arius.
The first element is more difficult to track down. It is quite obviously the word found in Latin piscis and Italian pesce, both meaning (and cognate to) ‘fish’—but its form and pronunciation doesn’t really match anything.
Italian pesce has the /e/ of pescetarian, but ⟨sc⟩ before a(n orthographic) front vowel represents /ʃ/ in Italian, and pesce is phonetically [ˈpeʃe]. This is different from English where pescetarian is generally pronounced /pεskɨtεəriən/2, with /sk/.
In Classical Latin, ⟨c⟩ always represented /k/, and piscis was phonemically and phonetically [ˈpiskis]; in later Latin as well as in English words derived from the Latin word, however, ⟨sc⟩ represented first the /ʃ/ of Italian and later on (in French, where English got most of her Latin words from) a simple /s/. Thus for example the Zodiac sign Pisces is /ˈpaɪsiːz/ in English, not */ˈpɪskiːz/ or anything like that. On the other hand, there are English words derived from the Latin word where the ⟨sc⟩ appears before a back vowel, in which case the pronunciation never changed and is still /sk/ in English. There are such words in Italian as well, where the Italian /e/ is maintained—but not in English.
The OED has a total of 43 words beginning with pisc- (excluding two for the liquor known as pisco (Collins), which is named after a Peruvian city whose name, according to Wiktionary, is from Quechua and thus unrelated). Of these 43 words, 26 begin with pisce- or pisci- and thus have no /k/ sound, while 16 begin with pisca- (14), pisco- (1), or piscu- (1). The pisco- and piscu- words (piscose and pisculent) are both marked as obsolete as are two of the pisca-, so basically, there are a handful of words beginning in pisca-, all pronounced /ˈpɪskə-/.
Contrarily, there is only one word in the entire OED beginning in pesc-, and that is pescetarian.
Both Merriam-Webster and the OED agree that in pescetarian, the first element is “probably” taken from Italian, but they cannot really explain why the word has /sk/ in English. The OED article says:
If the assumption that the word was formed on Italian pesce is correct, the pronunciation with /sk/ (rather than /ʃ/ ) and the spelling pescatarian both suggest that this origin has been opaque to many from an early date.
An alternative theory
Personally, I would suggest a slightly different scenario:
I believe the word was originally coined not from Italian, but from Latin, and I would hypothesise that whoever first came up with it in the late 1980s or early 1990s actually started out with *piscatarian, to go with adjectives like piscatorial (‘of or concerning fishermen or fishing’). Since the coinage was so obviously meant to be a ‘spinoff’ of vegetarian, though, the vowel structure of piscatarian was adapted to fit that of vegetarian; thus (showing only the vowels with “.” as the syllable separator):
vegetarian /ε.ə.ˈεə.iə/
piscatarian /ɪ.ə.ˈεə.iə/ ⇒ /ε.ə.ˈεə.iə/
Once the word started gaining popularity and entering wider usage, it was already pescatarian, and the link to the Latin root pisc- was somewhat tenuous and strained. Tenuous enough, at least, that people with limited knowledge of Italian started connecting the word to the Italian word pesce (often seen on menus in Italian restaurants) instead of the Latin root, and also began spelling it like the Italian word.3
The hypothetically ‘original’ spelling piscatarian (as well as piscetarian, of uncertain pronunciation) have appeared here and there in the early days; but they are far less common than the forms with ⟨e⟩.
Spelling preference
As for why one would prefer one spelling over another—well, that’s just personal preference. I personally prefer pescetarian because it maintains the same vowel skeleton as vegetarian not only phonologically, but also orthographically (and preferring in general British orthography, words like sceptic mean that I don’t find ⟨sce⟩ pronounced /skε/ all that unacceptable). One may equally prefer pescatarian because it is more intuitive for the ⟨c⟩ to represent /k/ before ⟨a⟩ than before ⟨e⟩ (especially if one generally prefers US orthography, where skeptic is not a parallel for ⟨sce⟩ as /skε/).
Notes
There is an awful lot of variation between who considers what ‘vegetarian’ and ‘non-vegetarian’. At one end of the spectrum are those who cling to the very narrowest possible definition of vegetarianism: someone who does everything they can to avoid eating, consuming, or otherwise using any part of an animal whose extraction directly or indirectly impacts the animal negatively: meat, skin, leather, ivory, etc. At the opposite end are those who call themselves vegetarian because they don’t eat red meat but do eat pork, poultry, fish, seafood, etc. I would say there is some leeway in how strict you need to go (I have no problem with calling someone who uses regular soap or wears leather shoes a vegetarian), but once your diet starts including the meat from animals, there’s little point left in terming it ‘vegetarianism’ anymore.
I’m using Wikipedia’s IPA notation for English to indicate phonemic writing here.
I imagine someone with proper Italian skills would not have done this, since they would be familiar with other Italian words that have [pesk-], like the verb pescare [pesˈkaːɾe] ‘to fish’. Assuming pescetarian is an urban American invention, though, most people who might use it are relatively likely to know pesce from restaurants, but less likely to know any other Italian words from the same root.
Best Answer
My answer addresses the first two questions asked above: "when the term prove or proof was first used for making breads," and "if proofing dough is AmEng or just a simple spelling variant."
A circuitous road to 'proof'
Prove in the baking sense appears as a separate meaning of prove in Joseph Wright, The English Dialect Dictionary, volume 4 (1904):
The source of Wright's entry has somewhat more to say about the words proof and prove, as used in Northamptonshire. From Anne Baker, Glossary of Northamptonshire Words and Phrases (1854):
Forby is Robert Forby, The Vocabulary of East-Anglia, volume 2 (1830); and as Baker warns, Forby has the "turn out well" meaning only in the sense of livestock:
But that particular meaning evidently goes back to at least the middle of the eighteenth century. From James Britten, Old Country and Farming Words: Gleaned from Agricultural Books (1880):
Britten's source for these glossary entries is Edward Lisle, "Observations in Husbandry" (1757) who uses both prove and in proof multiple times. For example, for prove, Lisle has these examples from his chapter on "Fatting of Cattle":
And for in proof, these examples from five separate chapters:
As these multiple instances indicate, Lisle and his contemporaries apply the term "in proof"—meaning something like "appearing vigorous, healthy, and thriving"—to both livestock and vegetation. Lisle's book was published by his son in 1757, but Lisle himself died in 1722, and he seems to have written much of the book in the first decade of the eighteenth century. Lisle's use of prove and in proof therefore represent very early instances of those terms in connection with a vigorous or thriving animal or plant.
Early instances of 'proof' and 'prove' in connection with dough fermentation
[[UPDATE: Mari-Lou A, who is responsible for the original post (above) about where "proving/proofing dough" came from, has also uncovered what are for now the earliest cited instances of 'prove'—twelve of them, in fact, in a single book—in the context of baking. Here is the first of these instances, from A. Edlin, 1805 Treatise on the Art of Bread-Making (London, 1805):
Edlin also introduces another relevant term, proving oven, described as follows:
So already in 1805, the author can speak of a type of "proving oven" as being "built upon the old principle." Regrettably, though a Google Books search turns up numerous matches for "proving oven" from the 1800s, 1900s, and 2000s, it doesn't find any earlier than Edlin. My thanks to Mari-Lou A for pointing out this extremely interesting book.]]
John White, A Treatise on the Art of Baking (Edinburgh, 1828) uses the term proof (in the sense of "dough fermentation") as though it were so familiar to his readers that he need not define it. The first of its multiple appearances in the book occurs without any fanfare:
Michael Donovan, Domestic Economy (London, 1830) provides an early definition of proof as a noun referring to the substance of the dough itself at a late stage before baking; unfortunately, Donovan provides no historical background on the term:
These two sources suggest that prove and proof were well established by 1830—and yet a very similar description of how to make yeast bread doesn't mention either term. From "An Experienced Method of making Excellent Bread," in The Gentlemen's Magazine (March 1758):
And likewise from William Ellis, "Of making common Wheaten-Bread for a private Family in Hertfordshire," in The Country Housewife's Family Companion (1750):
And earlier still, from a 1704 translation of Louis Lemert, A Treatise of Foods, in General (1702):
All three of these quotations describe the proving stage of the bread-making process, but none of them use the word prove or proof. This leads me to think that those terms became popular among bakers sometime between 1758 (the date of The Gentlemen's Magazine article) and 1805 (the date of A. Edlin's Treatise on The Art of Bread-Making).
Theories of 'proof' that are regrettably low on proof
The adulteration of bread (with chalk, alum, beans, whiting, and (in some cases human) bone meal or ash) was a major controversy in London in the late 1750s. For example, James Manning, The Nature of Bread, Honestly and Dishonestly Made ; and Its Effects as Prepared at Present on Healthy and Unhealthy Persons receives a fairly lengthy (and positive) review in The Critical Review (January 1758) that notes some of his tests for detecting adulterating agents used by dishonest bakers. The criticism led to regulatory legislation—"An Act for the Due Making of Bread: And to Regulate the Price and Assize Thereof; and to Punish Persons who Shall Adulterate Meal, Flour, Or Bread" (1763). But I could find no evidence at all that the use of proof and prove in baking had anything to do with the rising of the leavened dough as a sign of its unadulterated nutritiousness. The timing appears to be merely coincidental.
Another intriguing but probably false clue appears in Noah Webster, An American Dictionary of the English Language (1828), which includes this subentry under its entry for proof:
Might the bubbling of the fermenting dough during the last stage of rising have been equated with the "little bubbles" that appear as a result of agitating liquor? Again I have not found any evidence to support that theory.
'Proof' vs. 'prove' and 'proof the dough' vs. 'prove the dough'
In my Google Books searches, the earliest two references to proof (as opposed to "prove") in connection with baking that I found were from Britain (White's 1828 Treatise on the Art of Baking, published in Edinburgh, and Donovan's 1830 Domestic Economy, published in London). So it seems likely that proof got its start in Britain, or at any rate was in use there before it became especially popular in the United States. The term doesn't appear in any of the pre-twentieth-century dictionaries of American slang that I consulted.
The earliest match in a Google Books search for the phrase "proof the dough," where proof is a verb, is from J.M. DeWitt, "Red" in The National Baker (October 1915):
The National Baker was published in Philadelphia, Pennsylvania. Other early matches for "proof the dough" appear in publications from Minneapolis, Minnesota (in 1919) and from New York City (1920). The New York City example—Bread Facts, by Ward Baking Company, is especially interesting because of they way it jumps from proof to proving to proved in a section titled "Proving the Dough":
By way of a snapshot test, I looked at the first ten Google Books matches for "proof the dough" and the (only) eight Google Books matches for "prove the dough" between 1999 and 2015. The results: Of the ten books that used "proof the dough," one was from India and nine were from the United States; of the eight books that used "prove the dough," two were from Australia, five were from the UK, and one was from both. That suggests a strong split in preference between U.S. and UK usage.
Conclusions
I think that the likeliest source of proof and prove in connection with bread making is British colloquial usage of prove and in proof during the 1700s and 1800s to refer to the healthy growth, fattening, thriving, and vigor of livestock, crops, and trees. A similar enlarging of the dough as it sits and rises before being apportioned into pans and baked may have called forth the older rural term.
But the evidence is circumstantial at best. I haven't found any sources that claim a shared origin for the farming senses of prove and in proof and the baking sense of prove and proof. The closest thing to a direct link between the two sets of words is Anne Baker's Glossary of Northamptonshire Words and Phrases (1854), which identifies first the livestock sense of the verb prove and then the baking sense of the same word.
The Compact Edition OED (1971), though it contains definitions that allude to the colloquial farming notions of livestock that proves and trees that are in proof, doesn't seem to address the baking sense of prove and proof at all. I couldn't find any baking-specific examples, anyway.
As for "proofing dough," it does appear to be a predominantly U.S. alternative form to "proving dough"—and one that has emerged in roughly the past 100 years.