Sorry, you're asking the wrong question. The question should not be: do you think he has an alcohol problem? (This is what you were asking, right?) The question should be, "is this guy good for a mature, respectful, and loving relationship?"
Here are my thoughts: 1. does he have an alcohol problem? Maybe, maybe not. No idea. Who cares. That's his problem if he has one. If he has one, you should skedaddle. If he doesn't have one then he still has a problem that's worse than alcohol...
... he's abusive.
2. Is he relationship material? H3LL no. See above (he's abusive). You're 7 dates in and he's already belittling your opinions and showing you exactly how he would treat you if the relationship didn't work out (he'll call you "crazy").
You've only dated him seven times and this is the best he can act? Just walk away from this clown.
If you don't mind me saying, perhaps it is better to spend more quality time alone before dating again? 1 year is not long. You need to be able to trust yourself 100% before you jump into the shark pool. You may or may not have PTSD, but I think you should trust your intuition.