Is Buying a house in installments through banks?

Is it permissible for me to eat from the animal that I slaughtered for Allah to protect my family?

It is permissible to eat from the non-vowed animal sacrifice, and the person is rewarded based on the amount of meat that he had given to the poor. However, there is no evidence in Islamic Sharia indicating that slaughtering an animal protects one`s family, but it is a way for thanking Allah, The Almighty, for his grace.

My husband told me that he concluded our marriage with a fake name that belongs to another person, because he was sentenced. Nowadays, he recieved an ID, passport and birth certificate with the his current name. What is the ruling on being married to him?

Praise be to Allah, The Lord of The Worlds, and may His peace and blessings be upon our Prophet Muhammad and upon all of his family and companions.  As regards being married to the person mentioned in your question: The marriage is valid so long as he was the same person your guardian concluded the marriage with, even if he changed his name i.e. if your marriage contract was concluded with the same person, since what counts regarding marriage is the persons not names. And Allah Knows Best.

Is it permissible for a sick person to pray while sitting on a chair?

All perfect praise be to Allah, The Lord of the Worlds                                                                                                                                                                        It is permissible for a sick person, who is unable to stand up, to offer prayer while sitting on a chair. If he/she was unable to prostrate while on the chair, the he/she should pray while sitting on the ground, but if he/she was neither able to bow (Roku),nor to prostrate, then he can do them while sitting on the chair. And Allah Knows Best.