Actually, eleven and twelve also seem to be derived from 10+1 and 10+2. Let me quote from the classic book Number: The Language of Science by Tobias Dantzig (1930, republished with nice foreword by Barry Mazur):
Indeed, there is no mistaking the influence of our ten fingers on the “selection” of the base of our number system. In all Indo-European languages, as well as Semitic, Mongolian, and most primitive languages, the base of numeration is ten, i.e., there are independent number words up to ten, beyond which some compounding principle is used until 100 is reached. All these languages have independent words for 100 and 1000, and some languages for even higher decimal units. There are apparent exceptions, such as the English eleven and twelve, or the German elf and zwölf, but these have been traced to ein-lif and zwo-lif; lif being old German for ten.
And presumably this was inherited in other Germanic languages. (English, German and Norwegian all belong to the Germanic subfamily of Indo-European; French belongs to Italic.) Note that we can still discern a trace of "two" in "twelve".
That answers your question, but note that there are traces of other bases in our number words:
It is true that in addition to the decimal system, two other bases are reasonably widespread, but their character confirms to a remarkable degree the anthropomorphic nature of our counting scheme. These two other systems are the quinary, base 5, and the vigesimal, base 20. […]
Many languages still bear the traces of a quinary system, and it is reasonable to believe that some decimal systems passed through the quinary stage. Some philologists claim that even the Indo-European number languages are of a quinary origin. They point to the Greek word pempazein, to count by fives, and also to the unquestionably quinary character of the Roman numerals. However, there is no other evidence of this sort, and it is much more probable that our group of languages passed through a preliminary vigesimal stage. […]
While pure vigesimal systems are rare, there are numerous languages where the decimal and the vigesimal systems have merged. We have the English score, two-score, and three-score; the French vingt (20) and quatre-vingt (4 × 20). The old French used this form still more frequently; a hospital in Paris originally built for 300 blind veterans bears the quaint name of Quinze-Vingt (Fifteen-score); the name Onze-Vingt (Eleven-score) was given to a corps of police-sergeants comprising 220 men.
Also, we do have words like "dozen" (12) and "gross" (144) (any others?) for a few numbers not divisible by 5 (because highly divisible numbers are useful), but these words are sporadic and do not form the basis for any number-naming system in English as far as I know.
Edit: On further research, even though it's undisputed that eleven and twelve come from 1+10 and 2+10, the actual meaning of the lif part seems uncertain. The Online Etymology Dictionary confidently says:
c.1200, elleovene, from O.E. endleofan, lit. "one left" (over ten), from P.Gmc. *ainlif- (cf. O.S. elleban, O.Fris. andlova, Du. elf, O.H.G. einlif, Ger. elf, O.N. ellifu, Goth. ainlif), a compound of *ain "one" (see one) + PIE *leikw- "leave, remain" (cf. Gk. leipein "to leave behind;" see relinquish). Viking survivors who escaped an Anglo-Saxon victory were daroþa laf "the leavings of spears," while hamora laf "the leavings of hammers" was an O.E. kenning for "swords" (both from "The Battle of Brunanburgh"). Twelve reflects the same formation; outside Germanic the only instance of this formation is in Lithuanian, which uses it all the way to 19 (vienio-lika "eleven," dvy-lika "twelve," try-lika "thirteen," keturio-lika "fourteen," etc.)
But the OED says that "left" is just one theory:
Etymology: Common Teutonic: Old English ęndleofon corresponds to Old Frisian andlova, elleva, Old Saxon elleban (Middle Dutch elleven, Dutch elf), Old High German einlif (Middle High German eilf, German elf), Old Norse ellifu (Swedish ellifva, elfva, Danish elleve), Gothic ainlif < Old Germanic *ainlif- < *ain- (shortened < *aino-) [one] + -lif- of uncertain origin. Outside Teutonic the only analogous form is the Lithuanian vënó-lika, where -lika (answering in function to English -teen) is the terminal element of all the numerals from 11 to 19.
The Old English, Old Frisian, Old Saxon, and Old Norse forms represent a type *ainlifun, apparently assimilated to *tehun [ten]. The theory that the ending is a variant of Old Germanic *tehun, Aryan *dekm [ten], is now abandoned; some would derive it from the Aryan root *leiq or < *leip (both meaning to leave, to remain) so that eleven would mean ‘one left’ (after counting ten.)
It certainly wouldn't have been impossible for some alternate history version of English to have ended up with those abbreviations. However, we need to consider the things that lead to abbreviations happening at all.
The need for them has to be relatively common and they have to actually shorten significantly. If neither of those is true, nobody will bother to create the abbreviation.
To take root the need has to be relatively widespread. There is also a tipping point effect; up until a certain point the greater likelihood is that the abbreviation will just die out, but beyond that point so many people are using it that it becomes self-sustaining (the same as with any other term).
For the same reason, an abbreviation is less likely to gain currency if its need is already adequately filled by another. (A notable exception would be the many recent abbreviations referring to laughter, such as LOL, ROFL, PMSL etc. but there is a strong degree of deliberate play there, which encourages more permutations than would exist otherwise).
Now, both i.e. and e.g. are most often used in relatively formal writing that is putting forward an argument, or otherwise expositionary or scholarly.
At one point, such works would not be written in English, but in Latin. Only English people could read English for one thing, while any educated person in Europe could read Latin, especially considering the link between religion and higher education that once existed. Bede in the 7th and 8th Century wrote all his important works in Latin. Chaucer is "the Father of English literature" because he bothered to write in English at all, when most wrote serious works in Latin or French, and even he wrote his non-fiction in Latin. In the 15th Century Latin grew in secular use (ironically, the same Protestant scholars who rejected Latin in the prayer-book and the Bible, were particularly fond of it in the sciences, including most English scholars), and so scholarship continued to use it heavily. It began to decline around the start of the 18th Century (consider Newton, writing his earlier important works in Latin, his later in English), but continued to have considerable academic use until the end of the 19th.
And since all these people were writing in Latin, they would of course use i.e. and e.g. in the contexts they most come up rather than t.i. or f.e..
Now, any such academic writer would have a strong knowledge of the more commonly used abbreviations, along with scribal abbreviations, which are a form of abbreviation that combines letters and from which we get #, $, £, %, &, ‰, lb, &c. §. and indeed pretty much all of the oldest abbreviations used in English (etc. et al. ca. cf. ibid. op cit.) along with the practice of doubling for plurals (pp. for "pages", SS for "saints", §§ for "sections", etc.).
Note that while Latin was used throughout Europe, it had regional forms the same as English does now, and all the more so with abbreviations. For example, while both & and ⁊ were found throughout much of Europe, both being abbreviations of et, they survived in different languages (& used in quite a few as well as English while ⁊ is now pretty much only found in Irish and Scottish Gaelic in which & is not found).
These Latin-using scholars both used these abbreviations with which they were familiar both when they came to write in English, and if they came to teach English writing to others (and scholars was the pool of people from whom the best teachers were hired, after all).
For this reason, the abbreviations came to be known by literate English-speaking people even if they didn't speak Latin themselves. By this point, i.e. was almost as much a part of written English in a particular register than dog or cat was, and almost more a part of it in that register than that is!
It was at this point, when most people writing English in the register in which i.e. is used, that potentially t.i. could have taken over. But why would it? Why would people suddenly start using t.i. when the perfectly good i.e. that everyone knows would do a better job, because everyone knew it?
Latin also survived in different ways in other languages, such as the example of ⁊ in Irish and Scottish Gaelic I gave above. For this reason those expressions of Latin origin known to other speakers of European languages won't overlap fully with those used in English.
Best Answer
“Islam” is really just the one term for the religion that is most popular. Throughout the ages English has had many other terms for it, including some ending in -ism (definitions from the OED):
I’m not sure the reason why all of these went out of fashion. The forms that include Muhammad’s name are considered offensive because they put a mere human above god. “Islamism” and “Islamicism” are now also terms for fundamentalist or militaristic Islam, so it should be obvious why those two terms aren’t more used.
As for Christianity, the religion was originally called “Christendom”. The word “Christianism” was first used in 1576 and is still used as a nonce word when you need an -ism form according to the OED. There’s also “Christism” but that’s much rarer.
Surprisingly the term Judaism was only first attested in a1425 according to the OED. A slightly earlier term for it is “Jewry”.