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.
What is the ruling on someone who vowed to fast for two consecutive months, but failed to do so?
He is obliged to fulfill his vow by fasting for two consecutive months, but if he fails to do so then, it remains a debt on him until he either fulfills his vow, or dies. In case of his death, his guardian is supposed to fast on his behalf, or donate food from his estate in return for fasting, but if the guardian fails to do so then, it is all in the Hands of Allah.
Is my husband entitled to take my salary?
Your salary is yours, and you may give some of it to him as a kind of free-will contribution.
Should water be put in the deceased`s mouth and nose while washing him/her?
Putting water in the mouth and nose of the deceased while washing him is impermissible.