Has Islam made it incumbent on us to give our children particular names?
No, it hasn`t, but it is desirable that we give them good names.
Is it permissible for the young woman to turn the suitor down if she had no feelings for him?
Yes, it is permissible for her to do so.
Is a wife considered divorced if her husband refused to go to bed with her (for sexual intercourse) for two months?
A wife doesn`t get divorced no matter for how long her husband refuses to have sex with her, and she had better go to court.
Is it permissible for my brother, whom I had suckled, to conclude a marriage contract between his daughter and my son?
Such marriage is impermissible since one`s nephew in this situation is considered an uncle to one`s daughter; consequently, he is the brother of her father by suckling. In such cases, the people in question should go to court to prove the suckling.