Living in the same house after divorce

Yes, your father can remarry because he is legally divorced to your mother. Lot of couples decides to live together in the same house after getting divorce for various reasons. Your parents also did the same and now that your father wants to remarry, he can do so legally irrespective of the fact that he lived with your mother (his wife) even after divorce.

Alimony and maintenance can be claimed by the wife even after the divorce is finalized. In your parent’s case, the grant of maintenance to your mother depends on what is stated in Mutual divorce petition. If she had ceased the maintenance in that petition, she can't claim the same now.

However, if no such relinquishment clause was there, your mother can file a suit for maintenance in the court with the help of a lawyer. And upon showing appropriate evidences, the court may grant her maintenance from the ex- husband.