My 2 cents:
1.) I like the girl in the room, who is young and beautiful.
This one is correct, but it depends on available options as well. In some official problems you may found sentence with such usage inferior compared to OA.
2.) I like the girl in the room, the girl who is young and beautiful.
Absolute phrase modifier are powerful modifier. you are specifically pointing to that girl and modifying it separately and so no ambiguity exists at all.
3.) Peter hates to buy apples
...
1.) I like the girl in the room, who is young and beautiful.
This one is correct, but it depends on available options as well. In some official problems you may found sentence with such usage inferior compared to OA.
2.) I like the girl in the room, the girl who is young and beautiful.
Absolute phrase modifier are powerful modifier. you are specifically pointing to that girl and modifying it separately and so no ambiguity exists at all.
3.) Peter hates to buy apples
...
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