A:AnswerYes it's compatible I have been using it for little over a month and it works fine. I have a iPhone 7 Plus you just need to download the gear app from Apple Store.
A:AnswerYes, it tracks sleep automatically. I have attached a Photo of the "S Health" app that is used to view in depth information.
It also tracks floors, not necessarily stairs climbed, but I believe it uses the altimeter to measure increase in elevation. I have attached a photo of the "S Health" app as well.