Not Phil, but I’ll answer your questions as best I can. The “orthodox” flat earth model looks like this…
…with the North Pole at the center of a flat disk. Notice also the quasi-firmament of the sky, w/ the sun & moon cycling like the balancing elements of an old clock. What we know as Antarctica apparently forms the outer perimeter. One flat-earther in the documentary claimed that the outer rim is an enormous ice wall. I don’t know what happens if you start trekking across Antarctica…maybe your compass screws up because the entire perimeter is functionally the magnetic South Pole, so you just end up walking in a big circle.
As for your second question, I really cannot say. A couple guys on the documentary make reference to the Bible, but don’t appear to otherwise be overtly fundamentalist. Primarily, they seem to appeal simply to their own knowledge of this great Truth, rather than to any sort of scripture. So rather than the familiar YEC refrain of “we’re right, and God’s word shows that he clearly agrees with us,” it’s more of a “we’re right, because we’re right” kind of thing.