Does the clipping of nails nullify ablution?
No, it does not, and it is preferable to wash the hands afterwards.
An Imam stood to offer a fifth Rak`ah in a four-Rak`ah prayer, and he was reminded to sit by those behind him, but he wouldn`t listen. What is the ruling on those who followed his lead knowingly and intentionally?
If the Imam stood to offer a fifth Rak`ah, those praying behind him shouldn`t have approved of that, and the prayer of those who did is considered null and void.
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.
Should one obey his mother even if she was wrong?
Obeying one`s mother is an obligation in matters that are beneficial to her and so long as she didn't drive her children to commit an act of sin.