Can my boyfriend get his residency if I request after marriage?

It is not that simple. If he has a domestic violence felony conviction then he cannot adjust status even if you marry him; however if it is a misdemeanor then he may qualify under petty offense exception but burden is him to show that he is not a violent person, and overall, person of good character. If you marry him, both of you should genuinely want to be married to each other which generally requires living together day-to-day, paying joint tax returns, paying joint expenses, having joint bank accounts, and will be questioned w/tough questions on whether it is a bona-fide marriage. I strongly recommend that you consult with immigration attorney because of his conviction, and other prior immigration history.

He's going to have a number of potential issues. Generally if an individual does qualify for a legal status, it is best to apply before they are deported.

That is a tough one. If he was convicted of domestic violence, he may not have much of a chance. He would benefit greatly by talking to an immigration attorney.