Much like an encounter with a wild pet team, PVP Pet Battles are turn-based. However, unlike the PVE version, the PVP combat system is timed and any ability for each round must be chosen within that time limit otherwise it will assume you have passed a turn. A time penalty is applied if you take more than 15 seconds to choose an action, resulting in progressively shorter round timers for you.
You are right here. The Rematch string is part of the Info box, and as such it should be parsed correctly. (The string that contains the correct and breed/damage-specific min health requirements). This should be enough, but, I think there are also folks that aren’t using Rematch. They also should know of the type-specific min health requirements. Unfortunatly the default forms of the page don’t offer any detailed entries for the min health. They only offer one entry (for all damage types), and I always put the worst-case min health there (for pets that are weak against the expected damage type)