1. It's your problem, not my problem.
2. It's your problem, and it's not my problem.
3. It's your problem, but it's not my problem.
(What does #1 mean? Does #1 mean #2 or #3? Or do you have another expression which is the full form of #1?)
4. I think the girl (to be) her.
5. I think the girl (to be) she.
(Which one is correct?)
#1 means that "you" need to take care of the problem, not "me." In other words, whoever the speaker is doesn't feel responsible for whatever the other person did!
2 and 3 are grammatically OK, but not as smooth as 1.
5 is correct -- correct phrasing is "I think the girl is she." (Out of context, it's hard to tell what it means.) You use "she" rather than "her" because any form of the verb to be, when used as a main verb of a clause, requires a pronoun after it to be in the same case as a subject. Think of the verb "to be" as an equals mark in math. Here are some examples:
My brother is a retired mechanic.
My brother = a retired mechanic.
The cat is a ginger tabby.
The cat = a ginger tabby.
(Is Mrs. Smith there?) This is she.
(Is Mrs. Smith there?) This = she.
http://grammar.ccc.commnet.edu/grammar/verbs.htm#linking
1. The expression "It's your problem, not my problem" means that the issue or difficulty being discussed belongs solely to the person being addressed and does not concern the speaker. In this case, the speaker is distancing themselves from any responsibility or involvement in resolving the problem.
2. #1, "It's your problem, not my problem" means the same thing as #2, "It's your problem, and it's not my problem" and #3, "It's your problem, but it's not my problem." All three expressions convey the same idea that the issue at hand belongs to the person being addressed, and the speaker wants to emphasize that it is not their concern.
Regarding the second part of your question:
4. "I think the girl (to be) her" is the correct construction. The phrase "I think the girl" indicates that the speaker has an opinion or belief about the girl, and the pronoun "her" is used as the object of the verb. The sentence is implying that the speaker believes the subject of their thought or consideration is female.
5. "I think the girl (to be) she" is grammatically incorrect. In this sentence, the pronoun "she" is incorrectly being used as the object of the verb "think." To express that the girl is the subject of the speaker's thought, the correct pronoun to use is "her."