Should I require my boyfriend seek counseling?

Hello, I'd like some advice here for a pretty complex problem. My boyfriend is a kind, caring, (extremely) intelligent and sensitive person. I love him like no other. We've been together nearly a year but early on in the relationship I began to suspect that something wasn't quite right. He left his facebook account logged in on my phone one day after using it. When I went to check what I thought was MY facebook account, i see 7 or 8 messages, all to young, pretty girls about how he wants to cuddle with them, sleep next to them, etc. Some messages are more explicit than others. I confronted him immediately about it and he, of course, denied it. He completely emotionally shut down and didn't want to talk about it. Eventually, when I told him that I was not going to put up with this he gave me some weak excuse about it not being him who sent all of those messages, that he would never cheat on me, that it was a joke between friends that I didn't understand, blah blah. I told him that I was going against my own instincts by giving him the benefit of the doubt and that as long as he didn't do that again, I would never mention it again or hold it against him.

Three months later, something sent up a red flag for me that made me suspicious again. I don't remember what it was exactly that made me suspicious. At the time, my mom had just been diagnosed with an aggressive form of cancer. He knew about this, of course. While he was away I went through the email on his phone. I hated myself for doing that but I found a lot of really terrible evidence. For example, he had started an account on a dating site on my birthday, sent a bunch of messages on valentine's day to other girls, and had been answering adult personal ads on craigslist. The ONLY reason I forgave him for these things was because of the timing...these had all been sent prior to the ones I found on facebook. He swore that he had stopped doing that (and thus admitting that he had actually sent the facebook messages). I begged and pleaded with him to please just break up with me if he wasn't happy in our relationship and needed to go outside of it. He lives about an hour away so I end up spending a lot of my time with him instead of my family. I pleaded with him to just tell me the truth so that I could move on and spend that time with my mom before she passed instead of wasting it on a relationship that was destined to fail.

Now, three months later he has been an absolute ANGEL to me since that last incident. I couldn't ask for a better boyfriend.

Then, yesterday I get a message on facebook from a girl I've never met saying that my boyfriend is super creepy and had said a bunch of explicit things to her the night before. She forwarded me the conversation and I just wanted to die. I went all day swearing up and down that this was it. It was over and I wouldn't take any of his stupid excuses.

Well, when I confronted him he did exactly the opposite of what I had expected: he admitted it right away. He was completely forthcoming about having the urge to say creepy things online to girls when he's drunk. He was sorry and wanted to change. Then he proceeded to tell me that his father cheated on his mother with 6 or 7 different women throughout their marriage and that the few times his dad was home that he was usually beating him with a belt. He insists that all he wants to do is say these things, that he would never actually take it further than that. He doesn't understand why he has those urges but that they only happen when he's absolutely blacked-out drunk. He says that he hates that about himself and that it has nothing to do with me or our relationship.

My questions:

1) Should I believe him? Right now I do believe that he has finally decided to tell me the truth. The thing is, I feel like a fool. I never in my life thought that I would be taking someone back who has treated me like this.

2) Should I require him to seek counseling? He mentioned that he would be willing to go if I wanted him to. (He brought this up--not me).

3) Does childhood emotional/physical abuse/dysfunctional family cause this sort of behavior? What is it even called? I've tried to google "urge to shock people" as he describes it, but to no avail. I've also tried reading up on the effects of child abuse but haven't been able to pin down any sort of information on this particular urge. I feel like if we can actually understand the causes and why he is driven to do this, that we could get a better handle on it.

4) Should I worry that he could potentially become a sexual predator? It just worries me that he's doing this to random people to satisfy his urges. We talked a little bit about how these are PEOPLE who have feelings. He said that he understands that completely but still has the urge to do this, knowing how abusive that is to people.

Help?