I love to do yoga!  I find it so relaxing!
I love yoga too! My mother in law teaches Hatha yoga.
What exactly is Hath yoga?
Hatha Yoga teaches you to master your body and mind. I believe it focuses on strength and mental focus.
Does it include 'Hot Yoga'?
Yeah, you can do Hatha during a hot yoga class. I think you can do most yoga as hot yoga. Hot yoga just denotes the condition in which you are practicing yoga. 
Are there dangers to Hot Yoga?
I would imagine the danger of heat exhaustion increases with Hot Yoga, but you will have that with any physical activity done in hot or humid conditions