Hi Doudou. Sorry for the situation you are in. First things first!
You didn't Cause it, can't Control it and can't Cure it.
I would really suggest you visit the Friends and Family forum and check out the threads there:
https://www.soberrecovery.com/forums...ly-alcoholics/
You said:
I am confused on whether or not I should leave him for the cheating or its just really an alcohol/drug problem that needs to be resolved
I'm not sure why you are separating these two things. I don't know if he is an alcoholic or not, only he can judge that but he definitely appears to have a drinking problem, he uses cocaine and he cheats on you and abuses you.
This is not a recipe for a good relationship. Not all alcoholics/addicts cheat by the way.
Space and distance is really needed so that you can see this situation clearly, perhaps?
You can't save him from the drugs and you can't change that he cheated. All those things, the drug abuse and the lack of integrity and abusive ways are HIS problems, not yours (well they are now because you seem to have taken them on, but they are not yours really).
You deserve so much better than this.