The only cost in energy is when you are training your pets. It does not cost energy to be in either a practice match or a PVP match. So far, every time I have entered my pet in a match (practice or PVP) I have received something whether I win or lose. Of course, if I win, I get more than when I lose. There is no guarantee what Pet Snack and/or Pet Gear you will get for matching your pet with another - the result is random. As I understand it, PVP (pet vs pet) can provide slightly better snacks than practice matches but I have not noticed much difference. Part of the problem with PVP is trying to find another Pirate to have a PVP match with.
Pet training does not get you snacks. It uses them.
You can use Pet Snacks to help train your pets. Using a Pet snack will increase the amount of health, grit, guile, guts, and/or, sometimes, power that a pet has available when they fight. Training your pets allows them to go up levels. When you reach a certain level (10, 20, 30, 40, 50, or 60 - at the moment), your pet gets a Power or Talent added to his/her capabilities.
Another way to get Pet Snacks is to send your Companions out with Pet Wrangling orders. If you do this, understand that the Pirate you send out cannot participate in any fighting on quests until they finish getting what Pet Wrangling allows. There are some fights that you get into during your questing that, if you win, can give you a Pet Snack. It all depends on the enemies Loot Table and randomness.