I can only answer about the one I went to...
How many cats? 11, all I'd imagine from breeders as they're orientals, ragdolls, breeds like that that tend to be more interested in people.
And whoever asked about turnover, they don't seem to have much of one, the cats are all listed on their website and I've not noticed different ones particularly.
So you get the money back if they are all sculking in the back?
Nope, you just take your chances.
How do they stop them running out the door or someone trying to sneak one out in their bag?
You book, you don't just wander in like a normal cafe, so you're going in and out of a double entry system in small groups, supervised and putting on shoe covers as well.
What do you say if you get a hair in your tea?
Um, nothing?...
What if one bites you?
I can't really see how or why that would happen, it honestly is sitting about watching cats be cats, lol, some come over and try to steal cake, but there are staff there always... you're not really left to just harass them.