A liar and maybe cheater? what would u do if you in my case?

I've noticed my relationship never started good since the beginning (now 2 years). And thinking about all the things we've been through, I don't know if keep going is the best choice... At the beginning I noticed my boyfriend was in contact with her ex. I let it go trying to understand their break up, but then happened more times... (BACKGROUND: I believe he broke up with her because of me due to the times.... And she was maddly in love with him.  )So, The last time I found something, was that he sent her (his ex) some money o.o (they DONT have kids are never went married). I confronted him and he told me that she was desperate cuz she doesn't have money and he went to her rescue sending her money (she lives in other country).... What I don't understand is, how you could send money to your ex "if you don't talk to her/him in months?" Doesn't she have any friends or family in her country to help her? Why my boyfriend who is her ex?  Hilarious right? Then, other things have been going on, three weeks ago we fought so crazy that even the police had to come and chill us out, because I punched him in the face and he returned to me one :(  I don't think he is an aggressive person but he can't control himself when I start to fight and being aggressive. I went like this because all the things he did to me and he doesn't recognize that is his fault! Yes, I cheated on him many times because of my lack of confidence to him and he knew it and he is like nothing happens! That is driving me crazy, because if he knows I kissed my ex boyfriend, why he is so chill? I'm starting to lose my mind.......