All four sentences have problems!
1.) I like the girl in the room, who is young and beautiful.
I see what you're saying about "who," but from the position of the modifier, it still seems like you're trying to describe the room. If "the girl in the room" clearly refers to a particular person, like "the Queen of Spain," then you could say that the "who" part modifies that whole noun phrase. In a larger context, this could certainly happen. ("There are two girls--one in the room and one out. I like the girl in the room, who is young and beautiful.") However, since a GMAT SC will always consist of a single sentence, this doesn't work so well.
2.) I like the girl in the room, the girl who is young and beautiful.
The second "the girl" isn't redundant, as it fixes the problem in #1 above. If the GMAT were going to use this construction, it would probably use a long dash rather than a comma. (See, for instance, SC #95 in the 2nd edition Verbal Review.) However, this is really too much complexity for such a simple thought, and I don't see the GMAT presenting us with a choice like this. We'd be better off with "I like the young, beautiful girl in the room."
3.) Peter hates to buy apples from the market near his house, which the apples are too sour and expensive.
"Which" has to modify a noun. If you continue with a clause ("The apples are . . . "), you no longer have a modifier. Also, "which" should be modifying "house." This is 100% incorrect, and would never constitute an acceptable English sentence, on the GMAT or elsewhere. [ [Other than that, I love it.
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4.) Peter hates to buy apples from the market near his house, the apples which are too sour and expensive.
This is not similar to #3 but to #2, with all the same problems. (It's too complex for the simple thought it's expressing, and the GMAT would probably use a long dash.) I'll also second Piyush's point about "that" vs. "which." In this sentence (as, perhaps, in 1-3), it would work better to link with "because." "Peter hates to buy the apples sold at the market near his house because they are too sour and expensive."
(Notice that I made the first part more specific--"the apples sold at the market"--because otherwise "they" would refer to
all apples, rather than just those at the market.)