The most commonly accepted ideas, as far as I know:
What is the earth situated on or in if it is flat? ... What's under the earth if it is flat?
I personally don't know what the FET responses for these two.
Oh and last question - where do the poles fit into this hypothesis?
All believe the North Pole exists at the center of Earth. Official FET states there's actually a wall of ice stretching around the world at Antarctica and the South Pole doesn't exist. Dual Earth Theory says there's two separate planes, and the South Pole is the center of the "bottom" one.
Do you believe we are still in space? Is the atmosphere round or is that like a block above us? Do you believe in the atmosphere?
They do not believe we are in space, and many believe the atmosphere is somewhat round--there's the "atmolayer" contained by a dome-shaped Firmament that starts at that ice wall and reaches its maximum height above the North Pole, and the stars are beyond the firmament. All of it is above us. I don't know about DET's explanation.
I also know that there's a lot of different Flat Earth Theories because everybody's come up with their own personal ad hoc. This post is just a quick summary if the common ones. Especially for the ones about what's under the earth I'll have to let others fill in with what they believe.