You don't need a house for anything. If your Free Company has a house, you can buy a room from there, or buy an apartment from the newly added apartment buildings if you wish. By professions I think you mean crafting and gathering classes? Yes you can freely level those and your other battle classes as well. I would actually advice you to level your Warrior (Marauder) and White Mage (Conjurer) for the useful cross-class abilities (Foresight, Mercy Stroke, Bloodbath and Stoneskin) for your Paladin.