Ok there are a few quick rules pets go by.
1) You can only summon one pet at a time, does not matter if it is wolf, dragon, or a sin eater.
2) Your Pet can not return to your inventory if its food gage drops below 40%.
3) If your pets food gage drops below 55% you pet will feed itself.
4) To feed the pet you have to insert the food into the pet's inventory then use it there (Right-Click)
5) Beast shots should not be stored on the pet, to equip auto-shot, place the shots on your bar and Right-Click.
6) Resurrection spells that partially restore a player's XP will do the same for a pet.
7) If you equip a Pet with armor or a weapon it will automatically equip it the next time it is called.
8) You will gain Karma if your pet PK's another player.
9) If someone PK's your pet they will gain Karma.
10) Hold down Shift key when targeting a dead pet for resurrection.
11) When your pet dies, you have 20 minutes to resurrect it.
12) If you log when your pet is summoned your pet will return to your inventory.
13) If you Port or SOE while your pet is summoned it will port with you.

Leveling (Trained Pets):
All trained pets, but the baby pets, gain XP based on the damage that the pet does to the mob; the more the damage the more the XP. Trained pets will level the same as a "out of party" character, and will loosed XP and levels the same as well.

Leveling (Summoned Pets)
Summoned pet's levels are based from the level of the spell that casts this pet. The Summoner is able to increase the level of his summons by increasing the level of the spell. The summoned pets will drain a % of the caster's XP, depending on the pet.

Death (Trained Pets):
When a pet dies the player will have 20 minutes to resurrect the pet before the pet and the summoning item goes away forever. If the player leaves the game and comes back within the 20 minutes the pet will still be in its original location and with 0 HP, the pet will not return to the owner's inventory. If the owner does not login within 20 minutes of the pets death the pet will be gone forever.

When a pet dies it looses XP similar to a player, dead pets will also respond the same with Rez's as players do. Currently, within the game, there are Blessed Pet Resurrection Scrolls. To Rez the pet you will have to hold SHIFT down while targeting the pet.

Death (Summoned Pets):
Summoned pets do not loose XP and can not be Rezed, but are recasted by the Summoner.