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.
have an amount of 2,700 Jordanian dinars, which I have invested in a project, and I pay zakat on it every year. However, I have debts and obligations, and this project yields only a profit of about 2-4%. My salary is not enough to support myself and my family to the extent that I cannot pay the electricity bills. Is it permissible for me to take from the above Zakat?
You permitted to take from your Zakat since your income insufficient for you, because the poor is permitted to take from the Zakat in general, besides; the poor is identified of whose income doesn't suffice him. 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.
Am I Permitted to Use Ill-gotten Money given to me from Sorcerer's Sons during during my Mother's condolence?
You are permitted to use this money if you were ascertain that the majority of his lawful money surpasses the unlawful one. And Allah Knows Best.