Is the father a Mahram (Non-marriageable) to his son`s mother-in-law?

The father is a non-Mahram (Marriageable) to his son`s mother-in-law, so it is impermissible for them to look at each other, or to have a seclusion (Khalwah).

Is it permissible to trim the eyebrows if they become excessively long?

Trimming eyebrows is permissible if they become excessively long, yet; it is reprehensible. And Allah Knows Best.

What is the ruling on reciting the Chapter after Al-Faatihah , and what should a worshiper who forgets it do?

All perfect praise be to Allah, The Lord of The Worlds.                                                                                                                                                                  Any other part of Qur'an that a worshiper reads after Al-Faatihah during the first and the second Rak`ahs is a Sunnah, and forgetting to do so doesn`t nullify prayer, and doesn`t require performing Sujood As-Sahw (prostration of forgetfulness). And Allah Knows Best.

Is it permissible for a woman to perform the obligatory prayer immediately after the adhan and before the Iqamah is performed in the mosque?