the far east...
 

Does anyone know what is located WAY east; I'm talkin' off the map... and who exactly are the Easterlings and where do they reside?

More land. In which many Men live and they tend to serve Sauron out of fear. Easterlings would be included among these Men.

You know, that was an idea I had wondered too! They talk about the desert lands from there the Southrons and Easterlings come from, and it sounds like they are Arab terrorists or something! And then there is a discussion of the northern lands, where it is all snowy and whatnot.

All that begs a question: What shape is Middle-Earth? With the regions being the temperatures they are, I would think it would be round. But it sure looks flat to me.

I don't really see your comparison with Arab terrorists, Knight.

Christopher drew it flat, that's why. The world was made round once Ar-Pharazon (I think) tried to land on the Undying lands or something. Up til then it had been flat. But Aman was lifted up and Númenor sank and the world was made round.