Is this question asking "are you older than me?"? Or is" are you my elder" referring to an actual "elder" figure in the family/community?
Both in a way. It is literally asking if you are a person that is older than me (it must be interpreted as a older person/elder though and not just the adjective "older").
Nope, that is a different sentence. "Benden büyük müsünüz?"
It can be :) You can use nouns like adjectives in English.