Flat Earth Problems

I hear the "NASA lies" claim a few times from Flat Earth people, and it makes me wonder: does anyone actually believe Flat Earth views? For months I've been hearing about such positions, but I assumed that these were just atheist trolls having fun on the Internet. Apparently, that's not the case. So, here are a few problems for "flat earth" views:

1) Circumnavigation
There is not a "west edge" or an "east edge" of the world, except as defined by an arbitrary meridian, like the international date line. The modern "flat earth" folks seem to propose that instead the world is disk shaped, such that "north" is the center of the disk and "south" is the edge of the disk. I suspect the reason for this (instead of the opposite polarity) is that there are more commercial flights over the Artic circle than over the Antarctic circle.

2) South Pole
There is, however, a south pole. It's expensive to vacation there, but you can in fact go to the south pole. Just like the North Pole (when it's ice covered), you can go through all 24 hours of the day in thirty seconds or so. Some flat earth folks suggest that there is an enormous ice wall at the southern edge of the world, but instead you'll find a south pole. In theory, you should be able to charter a flight from Argentina to Australia, which could be directed to fly over the South Pole on the shortest great circle path (for example, there is a 12500 km / 7800 mile path over Antarctica from Buenos Aires, Argentina to Perth, Australia, which would be very close to going directly over the South Pole).

3) Southern Hemisphere Driving
Similarly, the disk projections of the world end up creating very distorted wide images of Australia, compared to the standard globe-based images of Australia. One could go to Australia and using a car's odometer to compare north, south, east, and west mileages between cities and see whether the projections align with the reality.

4) GPS
How on earth is GPS supposed to work if the world is not a globe. GPS works based on satellites circling the globe. You can actually get a map of their current positions (link). What's the theory here? They don't really exist? They are just flying around like airplanes? How do they stay up so long if they are not actually in orbit? Once again, if you want you can get a GPS receiver that outputs the raw data and actually see the messages from the satellites in the sky over you right now. You can then use math to get your current position from their messages. That's what a GPS device does to get your position, and it works with some amount of accuracy. Maybe NASA lies, but how could they possibly be making up GPS? Everyone uses it these days. You can even use it at the South Pole (granted that it's not the most ideal spot because the satellites are lower on the horizon there, but you can still use it).

5) Satellite Maps
How do satellite maps work? Why is it that you can go to some remote location, arrange fallen trees in an "X" and see it show up on Google maps in a short time?

-TurretinFan