Combat is turn-based and there is no time limit on each round in a PVE Pet Battle. You can take your time to determine which spell to use next. Some pet abilities have multiple round cooldowns, while others can do extra damage if certain conditions are met. Be creative and have fun testing which combination of attacks works best against different wild pets!
World of Warcraft Classic is currently in beta, which means some players are getting a chance to experience a much older version of the MMO ahead of its release. WoW Classic is based on how WoW played in August 2006, back around update 1.12. Back then, things were different. Tauren hitboxes were much larger, sitting could cause certain combat effects to not trigger and completed quests were marked with dots and not question marks. Strange days.
World of Warcraft Classic lets you play the game as it existed almost 15 years ago, upon the release of the 1.12 "Drums of War" update. Blizzard says it considers that era to be the correct balance of the game resembling its original launch state while also having ironed out some of the rough spots of launch. This version is also including some updates under the hood, like modern server infrastructure and Battle.net social features.
For the duration of the fight, creatures in the immediate area will not be visible to you (but they may still attack you if they wander too close). Keep in mind that other players will still be able to see you and attack you if you are eligible for player vs. player (PVP). Other players will also be able to view your pet battle in real time, including the pets involved as well as their health as the match progresses.