He lives in a house that his father bought through ribaa and gambling

The house that I live in with my family was bought by my father by bank and insurance company shares and their dividents (hence haram source). Is it permissible for me to live in it. If the answer is NO, then can I pay them rent on a reasonable basis.

Praise be to Allah, and blessings and peace be upon the Messenger of Allah:

If you can do without living there, then that is better. Otherwise, there is no sin in benefitting from it, and there is no need to pay rent etc., but you should advise your father to put right this wrong and to avoid these evil sources of earning.