If your pet's health gets too low or its attacks aren't very effective against a certain combatant, you can always switch out your current pet with another companion on your team. Only pets that are considered active (i.e., those in your three Battle Pet Slots), may be switched in and out during the battle. Once the match is over, you can always change up your active pet team, which is useful if one of your pets is low on health or dead.
Even though a modern server architecture is used, Classic servers won't have the same features that current World of Warcraft does. There won't be cross-realm servers or Looking For Raid and Dungeon Finder automatic party matchmaking. There are still a lot of questions about how the team will tackle it. This endeavor is being undertaken by an entirely separate team at Blizzard from the one working on World of Warcraft and its next expansion.
Each pet has 3 abilities it can use during a battle, but a total of 6 to choose from. They will also have a total of 3 active spell slots that show which abilities can be used during a Pet Battle. The first spell slot will already be unlocked, but the second and third will only become available once the companion has reached a certain level. Other spells will also unlock after reaching higher levels.