I've seen numerous explanations on east-west travel on this site. The premise makes sense, if you follow a compass west then the north pole will always appear on your right. Whether the earth is a spheroid or a flat circle, this holds true.

This does not, however, explain north-south travel. If you were to travel directly south in a straight line, by the flat earth theory you would come to the end of the earth once you hit the "ice ring" around the outside of the circle. What happens if you keep going? If earth is an infinite plane, wouldn't we have mapped out things past the ice ring by now? It would be statistically improbably for the only land masses on earth to exist at the center.

Also, direct south travel only gives more evidence to the earth being a spheroid. Imagine two travelers, one in Asia and one North America, at equal degrees latitude. Now imagine they both travel directly south at equal speeds, i.e. directly away from the north pole or center of the flat round earth. If the world is indeed flat, they would be  traveling farther and farther apart until they effectively reach opposite ends of the earth. Instead, gps and a multitude of other tracking technological advancements tell us that they are not in fact moving farther apart. As they move farther south, they actually get closer together in every way. How is any of this explained by the flat earth theory?

Also, assume we accept the theory of the flat earth for a moment. What is on the opposite side of the earth?  Do you assume that the earth encompasses the entire universe and there is no other side? If that's the case, than the earth Would still be a sphere, albeit a reversed one. If the earth is a continuous flat plane, how do you explain the molten core of the earth? Does there only exist fire and lava at infinitum for half of the universe?

These all seem to be questions unanswered in any of your linked materials or publications. I'd love to see someone explain any of these situations using actual scientific evidence.