1. Yes, you can do everything. You have to complete the level 10 class quest of the class you started as first, but after that it's as simple as changing your weapon.

2. You only gain experience for the class in which your weapon (or tool in the case of DoL/DoH) is equipped, so killing things as your Marauder (mr. great axe) is only going to yield XP for that class. DoL and DoH gain their experience from gathering and crafting.