What do minion level/speed/strenth/health do? I saw them when I added some minions to the minion zoo. Is there a minion battle place or something?

they don't really do anything, there was a planned minion battling minigame that never really progressed. any minion in your zoo that has stats, you can click on its picture and access the minigame still

Oh wow so that's what they do! I for a moment thought they're some kind of booster for pet battling (after not being able to find a minion battling tab anywhere), should've thought to click on the minion in the zoo!