On the question of the flatness of Arda, I find it interesting that there are a couple of passages in LoTR which seem to imply that the world is still, in some sense, flat. There are a couple of places where characters see incredible distances, such that the horizon really should have gotten in the way.

It's interesting, though, that in both cases I can recall there's a potentially supernatural element in the "sight." When Legolas sees the Riders of Rohan in detail at a distance of many miles, well, he's an Elf, and we know that Elven perception isn't always and entirely mundane. When Frodo sees all the way from Amon Hen to Barad-dûr, he's currently wearing the Ring and is partway into the world of shadows. In both cases one could read the character as extending perception into a realm in which the world is still in some sense flat.

All speculation, of course, since Tolkien never says anything explicitly in the text about it. I find it hard to believe that he didn't know exactly what he was doing in those passages, though. Tolkien had spent a lot of his life outdoors, and he had a lot of appreciation for the shape and feel of the natural world. He wouldn't have been unaware of how far away the horizon usually is.