-Are there any problems with a pill that has slighty dissolved in your mouth, before you managed to swallow it.

Not that I can think of, other than some un-coated pills might taste pretty bad.

-Any tips so i can swallow it, in one go?

Put it on your tongue and drink some water, that's what most of us do. Usually it just goes down with the water. Maybe start out with small pills first, maybe even some small candies like cinnamon hearts or tic-tacs.