Is my cousin committing adultery according to the Bible?

I have assumed from your question that the divorce was not a biblical divorce. The study "Biblical Divorce and Remarriage" describes what God considers to be a biblical divorce. A biblical divorce has the right of remarriage with God's blessing.

In brief, a biblical divorce is a divorce that occurred because the offending spouse committed sexual sin with someone else (bestiality, homosexuality, heterosexuality, or incest) or because the non-Christian spouse obtained the divorce. Anyone who has a biblical divorce has the right to remarry with God's blessing. Any other divorce or remarriage does not have God's blessing.

No. The woman must stay with the man. A man can have sex with women that are not his wife and still have a 'valid' marriage, however a woman cannot have sex with anyone other than her husband.

*According to the bible.

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