I rented an airbnb and the host asked me to sign a pool waiver release form including my name and address? Does this seem legitimate?

Yes, this sounds legit. They asked you to sign a pool waiver because they don’t wanna be held liable if you drown. They don’t know your swimming ability or if you will do anything dangerous. They don’t wanna pay your medical bills if you get hurt. 

Yes, it does sound totally legit.

Yes, it is legitimate and makes perfect sense and it is surprising that you can't see the liability of using a pool in a rental.

Yes. This person has the right to demand that you will not make them responsible for your behavior in their swimming pool when they are not home.This is considered a "private contract" between two parties and is legitimate in court in the future.

Hmm.. yes... if she didn't ask you for your Social Security Number, the number on your driver lisence, or your social security number.

They can ask you to sign anything. it may not be binding.