Welcome to SR, Dogluvah.
I can't tell you what to do, but I will tell you what I would do. If I was concerned enough at this point in a relationship to be asking these types of questions, I would end the relationship. I went into my marriage with "concerns", but I was so completely naive to this disease. Being married to an alcoholic has been the most incredibly painful thing. I would NEVER do it again and I would NEVER recommend it to anyone. The "little" issues never get smaller, they only get BIGGER.
I would run for my life.