Does the clipping of nails nullify ablution?
No, it does not, and it is preferable to wash the hands afterwards.
Is it permissible for a wife to refuse to go to bed with her husband (for sexual intercourse)?
It isn`t permissible for her to do so unless for a sound reason.
Is it permissible to openly announce the engagement of a woman who is in her waiting period (iddah)?
It is not permissible to openly announce the engagement of a woman in her waiting period (Iddah), but it is permissible to hint (imply) at it if she is in her waiting period after the death of her husband. And Allah Knows Best.
I married a man and had two children; however, we got separated four years ago. In addition, my husband`s brother, paternal uncle of my children, has been providing for them ever since. In fact, he is an honest, well-behaved man. Is it permissible that we get married although his brother (My ex-husband) is still alive?
All perfect praise be to Allah the Lord of The Worlds. May His blessings and peace be upon our Prophet Mohammad and upon all his family and companions.
It is temporarily prohibited for a woman to marry her stepbrother. Therefore, once she receives Talaq Ba`in (Irrevocable divorce), she is allowed to marry her stepbrother, even if his brother (First husband) is still alive. And Allah The Almighty Knows Best.