In BD if you click on an equipped item with a charm quality, a charm window will open. If necessary move the charm window so it is not over the inventory window, and then just drag and drop charms from your inventory (etc) to the charm window to permanently add them to the piece of equipment. For D2:ED I replied to your other post.

In both D2:ED and BD, learning a skill from a trainer increases the level cap, but does not give you any additional levels of the skill; you still have to add skill points yourself.