If he is abusive, then he needs to understand why he is like this, and find some way to fix it, before getting involved with you or anyone again. I can almost guarantee that the abuse won't stop unless he acknowledges his problem and does something about it.

The cheating is probably tied in with his abusive behavior.

I advise you NOT to go back with him right now, since it is a safety issue. Don't buy into the affectionate behavior that he is now displaying, unless he is making a huge effort to work on himself regarding the abuse and infidelity. He really should be going to a counselor for this.