Is my boyfriend abusive?

Okay, so I've been dating this guy for about a month and I've noticed things are starting to get really weird. I'll start from the beginning. On our first date we went to the Mall of America for a movie, shopping and lunch. We were not even dating yet, but anytime anyone would look at me he would grab my hand really hard like he was showing them I was his, maybe? Whenever we went in stores I wanted to look in the mirror to see if my makeup and hair still looked fine and he wouldn't let me he would stand in front of it or he would check himself out until I was annoyed with him and wasn't interested. After the first date we became a couple. Once we were together he always called me, texted me, asking me where I was, who I was with, anything. He lived about 10 mins from me but insisted we talk on the phone every night, skype every night and try and hang out every day. Whenever I told him I had plans with some of my friends he would make a huge ordeal about it and make me feel guilty for having friends or that I shouldn't be hanging out with anyone (and it was girls I was only hanging out with). We started hanging out more and then he told me he wanted to hang out in private, I was a bit weirded out with it and didn't buy the story he told me..but I went with it. The hangout spot he took me to was in the middle of the woods off of this freeway, it had a lake and everything but it was completely remote. After hanging out there twice with him I told my mom and even she was shocked about it, it was a really weird location to bring your girlfriend. So, I told him my mom didn't want me hanging out there anymore and he flipped out on me. He starting making assumptions and even said "I bet your mom thinks I'm some kind of killer or something, right?" and my mom and I didn't understand why he was so upset. Anyways, it gets weirder. I mean he was so extremely jealous of every one in my life. I was not allowed to talk to anyone but him, he was so controlling. One time, a guy posted a "truth is" on my Facebook telling me I was pretty and my boyfriend flipped on him telling the guy he would beat the sh-- out of the guy and so forth. That was also on our one month that he flipped out like that. I explained to him that I was his girlfriend and there's nothing to worry about and so much more and he completely ignored all that then texted me and said "Happy one month, baby :)" and when I tried to talk to him about it he acted as if nothing happened and didn't know what I was talking about. His dad is in prison for abusing his mother, so I could see where he would learn violent behavior..and his mom's ex step husband (who he now calls his dad) was a ex quarterback for the Packers and he was also extremely abusive to him and his mother...and my boyfriend even one time put a Facebook status up saying he "wants to be just like his dad when he grows up" and i don't know if he's talking about his step dad and his career or what? But that really put some strange thoughts in my head. While I was dating him, he bought me gifts and whatnot (he had money) and I think he did that to make up for how crazy he was, and to keep persuading me to stay with him. Well, I finally told him it I'm done with him the other day after all his craziness, and he flipped out on me telling me I'm the biggest piece of sh--, the ugliest thing even, no guy will ever love you and I'm a Christian and he knew I was and he even went far enough to tell me that I'm nothing but sh-- on the street to God. So I thought it was done there then, and that it would just be a nasty breakup, but we were never going to talk again. So I deleted him off Facebook, and deleted his number and on skype and I thought that was that. But a few days later he texted me saying his regular good morning text and had completely disregarded what had been said a few days ago..acting as if we were still together and I didn't respond to him at all..but later that night he showed up to my house ( and I had NEVER given him my address) so I don't know how he found out where I lived. But he came with his whole family and demanded I give him back all the stuff he bought me..and so I did it wasn't a big deal about that, I was just so creeped out that he knew where I lived? So that was just a brief discription of our relationship, do you think he was abusive? Or at least weird? I don't want to sound crazy or like I'm weird for thinking he was abusive..but I think he was.