Some of your questions are answered by this website, which contains a transcription of the original pamphlet describing biritch. Collison (the author of the pamphlet, and a railroad engineer who worked for a time in Turkey) apparently wrote a letter to The Saturday Review dated 28 May 1906, where he describes the history of the game. I quote:
Between 1880-4 I spent a considerable time in Constantinople and Asia Minor, where I played what was then called 'Biritch or Russian Whist'. I was then living, while in England, at Cromwell Road and introduced the game to many of my English friends, who liked it so much that they asked me to have the rules printed. ... 'Biritch' was attributed to the Russian colony at Constantinople; in my time the dominating social and political element. [not my ellipses, but the website's]
There were many variations of whist played in Russia, which this game was similar to. Mari-Lou in the comments has found a source that showing biritch is a variation of an earlier Russian game called yeralash. So while it's not clear whether the word biritch was originally Russian, most of the rules of the game are.
The word "biritch" means (in the game) no trump, although it is unclear whether this meaning is connected to its etymology. Maybe somebody who knows Turkish could tell us whether biritch might be a Russian mispronunciation of some word or phrase meaning "no trump".
More information probably can be found in the original version of The Saturday Review letter and also in another reference given on the above website: Thierry Depaulis and Jac Fuchs, "First Steps of Bridge in the West: Collinson's 'Biritch'", The Playing-Card, Vol. 32, no. 2, Sep.-Oct. 2003, pp. 67-76. Unfortunately, I can find neither of these online.
The first dictionary mention of all wet that I've found is from Wentworth & Flexner, Dictionary of American Slang (1960), which has this unsourced entry:
all wet Mistaken, misguided, wrong; esp. convinced of, portraying, or loudly arguing a mistaken idea or belief. Colloq. since c1930.
Chapman & Kipfer, Dictionary of American Slang, third edition (1995), has an even shorter entry, also unsourced:
all wet adj phr fr 1920s Incorrect; wrong. Your idea is all wet, I'm afraid.
The earliest discussion of the phrase in a Google Books match appears in John Alberti, "Weathering the Weather," in The Re-Ly-On Bottler: A Magazine of Ideas and Ideals for the Bottling Trade (June 1924):
Modern American slang is an institution that certainly merits as much approval as condemnation. It is so tersely expressive. But sometimes its application doesn't fit. "You're all wet," says the youth of today when he wishes to convey the idea that in his mind, your opinion or action or attitude in the matter under discussion is wrong. Just how the expression gained its vogue, or how it came to acquire its peculiar meaning is something outside the limit of my education along this line, but I imagine that it has some connection with the older expression regarding the person who "doesn't know enough to come in out of the rain."
By 1925, the expression was well enough established in U.S. popular culture that humorists could use it as a punchline. From "Old Stuff," a joke originally published in Life magazine, reprinted in the DeKalb [Illinois] Daily Chronicle (November 13, 1925):
HISTORY TEACHER—And what did Hero say to Leander after he swam the Hellespont?
THE KID—You're all wet!
Going back to 1918, we have this instance from Arthur ("Bugs") Baer, "Keeping the Wolf Away From the Yale Lock," in the [New York] Evening World (December 14, 1918):
While John Husband was out making the works safe for Democracy's wives [by fighting in the Great War], what happened?
Why Democracy's wives swiped Democracy's jobs. And Democracy is going to have a jazzboed time getting those jobpieces back. Friend wife has been holding down Comrade Husbnd's job and she is now hep to the cinch that the lil' fat rascal had. No more chance of hubbo coming back and grabbing off two tens for a five on that work stuff. The wiff has held his job down for two years. And she is wise that the fifty-fifty stuff they pulled at the altar was the bunk. It took a war to make Lena see that she was getting shortchanged by about forty-nine on the fifty-fifty arrangement.
The bird who used to get away with the salve about being overworked is out of luck. He's all wet.
It seems clear that "all wet" is a choice element in the latest slang, circa 1918, along with hep, bunk, cinch, jazzboed, wiff, hubbo, and such kindred terms (noted elsewhere in Bugs's article) as "the darb," "the grand razz," "you buzzed it," kerflapped, and zapps.
Another early occurrence (with a different implied sense of "all wet") appears in David Lustig, La Vellma's Vaudeville Budget for Magicians, Mind Readers, and Ventriloquists (1921), in the context of an extended bit of comedic patter to accompany the "Wine and Water" trick, where the magician changes a glass of wine successively into a glass of water, a glass of darker wine, a glass of milk, a glass of whiskey and finally a glass of water again:
Now kind cash customers....I will let you in on a little secret (takes pitcher in hand). Chemists claim that home brew....you know, raisins soaked in water....is poisonous. I have no doubt of it because a friend of mine recently drank a number of glasses and they carried him home dead....drunk!
Your friends will tell you there are all kinds of drinks concocted nowadays....and along comes a fellow just before I came out here....who claims he knows a former bartender who makes his own beer and calls it Male beer....and why? Because this bartender's name is Cohensky and the beer is Hebrew (he-brew).
Mr. (names theatre) close this act.... he's all wet! (aside) No such luck. Can't get enough of it nowadays.
Here I suspect that the phrase "he's all wet" may be intended to signify "he's drunk"—and it isn't hard to imagine a progression from telling a drunk who is being loud and unreasonable, "You're all wet!" and telling a sober blowhard who is being loud and unreasonable, "You're all wet."
In that regard I note that Wentworth & Flexner have this entry for wet as a stand-alone slang word:
wet adj. 1 Inferior or objectionable in any way; unpleasing; worthless; stupid; unfashionable, as in dress or manner; overdressed; boastful; etc. 1924 ... 4 Drunk. Not common.
Another possible influence on the emergence of "all wet" is the term "wet blanket," which Christine Ammer, The American Heritage Dictionary of Idioms, second edition (2013) says dates to the early nineteenth century:
wet blanket A person who discourages enjoyment or enthusiasm, ... This expression alludes to smothering a fire with a wet blanket. {Early 1800s}
Still, Alberti's argument in the June 1924 Re-Ly-On Bottler that the phrase "all wet" alludes to the expression "doesn't know enough to come in out of the rain" is appealing, too.
Best Answer
Antecedents of 'game-changer'
For many years people have discussed the effects on various sports and pastimes of introducing innovations in rules, equipment, personnel, or tactics in terms of their potential to "change the game." For instance, "Concerning Rules and Regulations," in The Yale Literary Magazine (January 1905) offers this commentary on football:
And "Effect of Inventions upon Sport and the Trade," in Hardware (December 25, 1906) contains this discussion in connection with golf:
It stands to reason that as discussions of "changing the game" continued over the decades, someone would resort to "game changer" sooner or later.
Early occurrences of the term 'game-changer' used in a literal sense
The William Safire column mentioned in Josh61's question is from the New York Times of September 12, 2008. The paragraphs relevant to the question of when the term was first used literally and figuratively are as follows:
I can't find a copy of the 1930 Atlanta Constitution article online, but it appears to be using game-changers in the literal sense of "ones who are changing the game."
Safire cites a 1982 Washington Post story in which Ken Singleton of the Baltimore Orioles had a "game-changer"—that is, a hit that effectively changed the particular game in the Orioles' favor. Here "game" refers to a specific contest—a particular baseball game, rather than the game of baseball itself. The description Safire cites from a decade later of football player Desmond Howard as "a game-breaker and a game-changer" refers to Howard's ability to break open a close game with kickoff return, a punt return, or a long reception. Thus "game-breaker" here refers to a particular player, not to a particular play.
Even more suggestive is this item from Inside Sports, volume 3 (1981), which also appears in Thomas Boswell, Why Time Begins on Opening Day (1984) [combined snippets]:
The usage here is similar to the Desmond Howard usage: the focus is on a player who is capable of altering the outcome of individual games. But there is also a sense here that the player is altering the broader game itself. Just as a certain type of tight end altered the way U.S. football was played in the late 1970s (which the article earlier alludes to), the emergence of a type of agile, power-hitting third-baseman is altering the way successful baseball teams are being put together and managed. So here we have an instance where game-changer refers in part to changing the sport itself and not just a particular contest.
I note, however, that the first two editions of Paul Dickson, The Baseball Dictionary (1989/1999) do not to have an entry for "game-changer," strongly suggesting that the word/phrase was not, as of 1999, an established, baseball-specific term of art.
'Game-changers' and 'game-changing'
We've seen that a game-changer is a game-changing event, player, or (in a figurative sense) idea. From this, it follows that instances of the term game-changing might be important precursors of the noun game-changer. But Google Books search results turn up few matches for game-changing as an adjective prior to the late 1990s. The exception appears in Charles Savage, "Comments" (a response to Stanley Krippner, "Consciousness-Expansion and the Extensional World"), in Et Cetera (December 1965) [combined snippets]:
The context here is evidently the highly theoretical world of "the game model of behavior." (The "Harvard controversy" mentioned in the second paragraph, by the way, refers to experiments conducted in 1960 and 1961 investigating the effects of psilocybin and other hallucinogens on Harvard undergraduates.)
In addition, one early instance of game-changing used as a noun appears, in Esquire magazine, volume 82 (1974), reproduced in George Leonard, The Ultimate Athlete [combined snippets]:
Although the idea of "game-changing" here is unusually theoretical, it clearly accommodates the idea of a game-changer as a person responsible for leaving a game (in the sense of a sport or pastime) and starting a new one.
First definite use of 'game changer' in a figurative sense
As Mari-Lou A points out in her answer, the earliest Google Books match for game changer used in a purely figurative way is from Catherine Hayden, The Handbook of Strategic Expertise: Over 450 Key Concepts and Techniques Defined, Illustrated, and Evaluated for the Strategist (1986) [combined snippets]:
Conclusions
The notion of "changing the game," in the sense of altering the fundamental way a sport or pastime is played, has been discussed in published texts going back more than a hundred years. The adjective "game-changing" appears at least as far back as 1965, in a highly analytical context involving the game model of behavior; and game-changer used in a literal sense may go back as far as 1930 (in the context of the card game bridge, according to research noted by William Safire) and certainly at least as far back as 1981 (in the context of a discussion of revolutionary changes in the use of certain positions on the field in baseball and U.S. football).
The first confirmed figurative use of game changer in Google Books search results involves business jargon (reported in 1986), where it refers to an innovation that alters the competitive landscape in a particular industry or market.