Is it healthy to drink 6 glasses of skim/low fat milk every day? Because I'm trying to gain weight. By the way I'm not lactose intolerant.

Not bad but... 8oz of skim milk have 80 calories in them, so 6 glasses a day would be 480 from the milk alone. Depending on how much & what else you eat, this may be more than you want. Otherwise, it's not a problem.
Should be ok. Skim milk is a responsible choice (unlike milkshakes or other junk food). The one thing to keep in mind is to do strength exercises to help gain muscle instead of fat. Even people of normal size can have problems with heart disease.