No, they are not interchangeable. #1 asks if the brother is at the other person's home, which #2 asks if the brother is with the other person. The brother could be at the other person's home, even if the other person is not with the brother. And, re #3, the brother could be with the other person, but somewhere other than the other persons' home. #2 seems to imply that the other person kidnapped the brother. That is the only situation in which an English speaker would refer to someone "having" another person.

Hi Sasha, you can say: I really like/enjoy spending time with my family because they are fun to be with and will support me when times are hard/and will support me through my difficult times/and will support me when I'm going through tough times or through a difficult patch. Corrections given according to British English. 😉

Pelin, you can ask/say: Is my brother with you or Is my brother at your place? Although it is grammtically correct to ask, Do you have my brother? it sounds unnatural/weird to me, as if you were asking the other person/people if they had kidnapped your brother and were holding him to ransom.