ANSWER:

He is living in zina with this woman as a muslim man can only marry a muslim woman, or a chaste Christian or a Jewish woman.

He cannot marry a polytheist and he will be sinful if he did while acknowledging that such a marriage is invalid.

If he believes that the marriage is valid while being shown the evidences of the Quran, Sunnah and the consensus of scholars that such a marriage is invalid yet he still says it is valid, he is an apostate and his prayers, Hajj and Umrah are all invalid. 

Can a Muslim man married to a polytheist perform umrah or hajj?

Fiqh of Marriage, Invalid Marriages | April 7, 2019 1:51 am
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Sheikh, here in my community people used to have many feast festivals during maraige and after marraige like feast functions on 2 day of wedding similarly on 7th, 10th etc where(israf) lot n lot of food is served and most(tons) of the food goes waste. Is it permissible to attend these functions.
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Shiekh I have a sister who converted to Islam six months ago she now see a man whom she love and want to get married to him BUT her father said no only. her mother and uncle say Yes. it’s permissible to get married without her father permission?