Etymonline has this to say on quarters:
"military dwelling place," 1590s, from quarter (n.) in sense of "portion of a town." The military sense is in quartermaster (mid-15c.) and might be behind the phrase give (no) quarter (1610s), on the notion of "to provide a prisoner with shelter." The verb quarter "to put up soldiers" is recorded from 1590s.
Quartermaster appears to be from something unrelated to fourths:
mid-15c., from Fr. quartier-maître or Du. kwartier-meester; originally a ship’s officer whose duties included stowing of the hold; later (c.1600) an officer in charge of quarters and rations for troops.
Although I am weak at French, it appears that quartier means area or district. Note that the dates for quartermaster are before quarter: mid-15c versus 1590s. This implies that quartermaster transferred first and then people began using quarter due to the use of quartermaster.
Transferring the meaning of quarters into a non-military dwelling place seems reasonable and, therefore, the short answer to your question is that quarters appears to have come from France by way of quartermaster.
Edit: My hunch on why quarter came from quartermaster (as opposed to Etymonline just telling us it did) is the inclusion of master in the term led people to assume that they were masters of something; it was logical to call that something a quarter. The idea of quartering up soldiers would mean to provide for them; this would be the quartermaster's responsibility. Lodging was most likely included in that and the perception of "master of lodging" makes sense.
J.E. Lighter, The Random House Dictionary of American Slang (1994) reports that the origin of bitching in a positive sense was student use:
bitching adj., ... 2. Stu. excellent, wonderful, exceptionally attractive. Also, bitchen.
[First two cited occurrences:] 1957 Kohner Gidget 10: It was a bitchen day too. The sun was out...in Southern California. 1962 English Jrnl. (May) 323: Bitchin' equivalent to neat or swell.
The instance in Frederick Kohner, Gidget (1957) reads in context this way:
I tried it. I was sort of desperate to write this story so I drove out to the main drag (I got my junior license only last week) all by myself, and I took that pencil and notebook along and was all set to begin at the beginning. I mean with the description of the place. It was a bitchen day, too. The sun was out and all that, even though it was near the end of November. But then, we are living in Southern California and if you wouldn't look at the calendar you'd hardly know the difference—honest!
Gidget is a surfer-girl novel, written by the real-life father of the original gidget (gidget, we learn, is a surfer palindrome for "girl midget"). A discussion of the book and of the California surfer subculture of 1957 in "Gidget Makes the Grade," in Life magazine (October 28, 1957) reveals another instance of bitchen in that subculture:
The book tells how Gidget learned the difficult art of surfboarding—catching the "bitchen wetbacks" (big waves) and "shooting the curls" (riding the surf) without "getting the ax" (falling under a breaker). An indomitable girl, Gidget finally masters the board.
I don't recall ever having encountered the term wetbacks except as an derisive (and offensive) name for braceros—unlicensed Mexican nationals who cross over the U.S.-Mexican border to pick crops and perform other hard labor in the United States. (The term wetback refers to their having supposedly crossed the border (illegally) by swimming across the Rio Grande, which forms the entire border between Texas and Mexico from Brownsville/Matamoros on the Gulf of Mexico to El Paso/Ciudad Juarez in far west Texas.
In any event, the positive sense of bitching can apply to bitch as well, as this glossary entry in "The Parlance of Hip," in Esquire, volume 52 (1959) indicates:
BITCH: something very good. Example: That song is beautiful. That musician has a bitchin' ear. Bitch also means girl or woman, but not in a derogatory sense. Example: I've got me a fine bitch.
The "not in a derogatory sense" language here may be intended to indicate that a a person using the term may not mean to convey the idea that the girl or woman so designated is unpleasant or unattractive in any way, but the notion that "bitch" is therefore not derogatory appears to be a relic of a particular (and peculiar) male view of the subject at the height of the Mad Men era.
And a glossary in the Saturday Evening Post, volume 234 (1961) has this entry for bitching, along with entries such as "like wow," "like cool, man," and "swinging":
bitching — joyous term, as in: "I had a bitching (or joyous) time."
Wentworth & Flexner, Dictionary of American Slang (1960) find an even earlier antecedent for bitching in a positive sense in bitchey:
bitchy, bitchey adj. 1 Having the attributes of a bitch. 2 Striking in appearance; classy. 1930: "A pearl-gray Stutz, a bitchey roadster, all right." J[ames] T. Farrell, 137. Some c1930 use.
The Farrell citation comes from a short story called "Looking 'Em Over" (1930).
It's not impossible that the use of bitchin' in 1950s surfer lingo directly recalls the early 1930s usage of bitchey in a similarly upbeat sense. But it may be even more likely that the adjective bitching (or its more elaborate sibling son-of-a-bitching), popularized by soldiers during World War II and the Korean War, provided the inspiration for the newly positive bitchin'. In any event, it seems truer to attribute its origin to the surf lingo of Southern California in the late 1950s than to student use, as Lighter unaccountably does after noting its early occurrence in Gidget.
Best Answer
J.S. Farmer & W.E. Henley, Slang and Its Analogues, Past and Present, volume 6 (1903) offers this interesting entry for scoop:
A 'scoop' on Wall Street
The 'Change mentioned in the second noun sense of scoop in Farmer & Henley's entry for the term is the New York Stock Exchange—and this slang usage turns out to be considerably older than you might suppose from Farmer & Henley's description. A lengthy description of what the term refers to in its Wall Street slang sense appears in "Financial Items," in the [Philadelphia, Pennsylvania] Evening Telegraph (August 4, 1868):
From the "New York Money Market," in the [Philadelphia, Pennsylvania] Daily Evening Bulletin (February 22, 1869), reprinted from the New York Herald:
From "Financial and Commercial," in the [New York] Sun (April 15, 1871):
And from "Slang of the Stock Board," in the Nashville [Tennessee] Union and American (January 17, 1873):
A 'scoop' in the press
The earliest Elephind match I found for the noun "scoop" in the sense of a journalistic exclusive story is from "The Night Reporter," in the Columbia [Pennsylvania] Spy (May 28, 1870):
Conclusions
Elephind newspaper database searches yield first occurrences of scoop as a Wall Street slang term for a type of stock price tampering from August 4, 1868, and of scoop as a newspaper term for a major exclusive news story that appears in print before the competition's coverage of the same event does from May 28, 1870. I don't know whether these overlapping slang usages are etymologically related or merely coincidental.
At least superficially, the Wall Street "scoop" suggests undercutting a stock's price in order to buy the stock later at a distressed sale price, while the journalistic "scoop" suggests getting the first shot at plunging a hand-held scoop into a barrel of something good before one's rivals have a chance to dip into the same barrel themselves. On another level, though, both slang terms seem to involve a notion of having valuable information that no one else does about an event or developing situation.
If one slang usage emerged from the other, I think it more likely that the journalism scoop derived from the stock market scoop than vice versa. But both may have arisen independently, from two fundamentally different senses of a literal scoop: a low point or depression (as in "a scoop of the sloping hills"; and an implement full of gold, meal, or some other desirable commodity.