Multiple Pets and World PvP

Keep in mind that the following developer responses are from the beta forums. Things are subject to change and there may be updates to the mechanics mentioned below before the official release of MoP.

Limitations On Multiple Pets
A recent blue post seems to indicate that while players will be allowed to have multiple versions of most pets, players will not be able to keep more than one version of some uniquely obtained companions. [source]

Yes, you will be able to have 3 of almost every pet. Certain pets are unique since they are attached to a Wow license, granted from an achievement or earned from TCG codes.

World PVP In Pet Battles
In another blue response, it is revealed how developers currently plan on addressing the possibility of players encountering world PVP while engaged in a battle with a wild pet. [source]

The fact that players are vulnerable to PvP attacks while in a pet battle is intentional. However, a couple features that go along with this are not implemented yet.

First off, the exact pet you were fighting when you were broke out of pet battle will be respawned. Same quality, stats and skin color. Second, you will get a 3s damage shield that absorbs 50% of incoming damage to help negate the fact that you need time to recover after exiting the pet battle interface. Both of these will be in for the next build.

We feel its very important to keep the PvP aspect of the game intact and if you choose to play on a PvP server, you will certainly be fighting for those rare spawns. (This rule effects PVE servers as well but only in contested areas.)