Biting your finger Shouldn't hurt your frog unless you do something silly like prying it off or dropping it. You just need to be aware of the possibility of a bite when you put your hands near them so you can avoid jerking away and hurting them (they're fast too, so it's pretty hard not to startle sometimes!). The bites really aren't that bad though. About like getting a stubbed toe.
I think they really do recognize their keepers. I've been 'stuck' by Trevor's tongue several times, but she has always detached without biting, like she realized she made a mistake (or maybe I don't taste good, idk).
She has drawn blood from other people that she doesn't like before though lol. It's kind of hilarious really. Everyone else is afraid to go into her tank.