Is it permissible for a Muslim woman to wear trousers at home?
Wearing trousers at home isn't prohibited so long as non-Mahrams do not see her. And Allah Knows Best.
I suffer from absentmindedness and constant worries during prayer, what should I do?
You should take refuge in Allah from the whispers of the devil and life worries. You should also seek Allah`s help and offer a lot of Istigfar (seeking the forgiveness of Allah). And Allah Knows Best.
Is it permissible for a woman who is in her confinement to fast upon seeing blood signs that are neither black, nor red ?
Brownish, reddish, and yellowish discharges are all considered confinement until there is no colored discharge which marks the end of confinement. Moreover, the aforesaid woman is prohibited from fasting until she attains ritual purity. And Allah Knows Best.
Is the marriage contract considered valid if concluded at home by the marriage official (Ma`zon)?
Yes, it is valid as long as it is registered at the court.