Hello! Looks like you have companions on Kayu and Jitsu. You can play with them on the wolf's page. That and bringing companions on campaigns will help you level them. Also, if you have multiple of the same companion, it will level faster.
Unless you have more companions, you won't be able to add one to other wolves. Or you would need to remove the companion from Kayu or Jitsu and move it to a new wolf.
Forum > Game Guides
Has a lot of good guides on everything from cooking to campaigns to the arena.
I recommend Icerun Sword 1 (Windborne's Retreat) for leveling wolves/companions. It's great for food because there's a single encounter that can get you 6 catfish to cook. Battle sequences can be refreshed through without losing rewards. So long as you click 'Attack' before refreshing and your party is strong enough to win you'll still get the rewards but save yourself a lot of time.
If playing on a computer also recommend using multiple windows when playing for better efficiency. You could theoretically resize a bunch of windows with all the different professions in them to fit on your screen. Personally I just play with two though. A large one for campaign and a small one for cooking so I can visually see whenever I need to refill the pot.