1. The planets in our solar system are round. Earth is not a planet, so it's not round. There are many reasons Earth is special, including being the center of known intelligent observation of the universe.
2. Not sure there is one for sure. Some definitely think the photos of other places are real, but just don't come from a space based device. Others lump them all in with the rest of the images coming from space based devices (fake)
3. For those still using the unipolar map, nobody knows. The bipolar map has Antarctica as a second continent, and thus can fit the base. What is around the edges is still unknown however.
4. That is one possible theory. As for falling off, it is unknown both if it's possible and where you would end up (other than below the Earth.)
5. Various answers have been proposed, from balloon carried satellites, to troposcatter relays. Note these are the same methods proposed for Satellite TV.
I think a better question for these maniacs would be to ask: When we look through telescopes and view other planets and celestial bodies, they, too, all appear to be perfectly round. Is the suggestion, then, that these discs are all perfectly aligned with the Earth, facing directly towards us?
They are sphere's, not flat like the Earth. The Earth is not a planet, and as such doesn't follow the same rules. If you have 5 objects in a room, and four of them are chairs, should we just assume the 5th is a chair as well and not a table?