SNIP

So how do top loading dryers work? I've never seen one.
^^^

Take a look at http://fisherpaykel.com/product/laundry/dryers/

Are there 2 doors, one on top of the cabinet and one on top of the
drum?

I assume the drum still spins horizontally so the contents can tumble,
so I assume there must be a door on the drum.

Yes and Yes

Does the drum door always end up on top when the dryer stops or do you
have to manually spin the drum to bring the door to the top?

Drum is made to stop with door on top, and open at end of cycle. If
power fails, there is a procedure to force the drum door open