He's looking for a cheap thrill, in the midst of this pandemic. Can't do anything physical, so looking for something else to bring some excitement to his life.
He clearly wants to deceive you, because he keeps saying he is single. How does he chat throughout the night? Easy, he just says he is doing his assignment/work.
The point is, he is definitely lying. To you and to his wife.
If you need his input to finish up the assignment/course, then keep it to that. Don't be surprised he will MIA one day.
Chatting with married guy