It was 50HP, so if they have 50 HP and end their turn on the mountain, they die
No, religious city states are essentially like Cultural - you get faith points
I haven't heard anything about holy cities. So I'm guessing you're religion is always yours and you can't lose ownership of it by losing a city. Makes sense since you can't found two religions you they wouldn't then let you capture one.
After a certain number of faith points there is a chance you will spawn a Great Prophet. You use the GP to found a religion