Bear in mind that, while we're crossing a whole continent right now, it's quite likely that in future expansions we'll be traveling to the lands between. If there was a big skybox difference between Eorzea and Othard, once we started tooling around these middle areas we'd need to see a gradient of these extremes - and that just starts to get way complicated. Additionally, Eorzea time or not, a lot of players are going to be confused when it's dark out at 10am, or whatever. It's easy to see why SE just decided to handwave the whole issue. If you like, just pretend that the whole transport process actually takes several hours and is not instant - that could account for the time difference.

On the topic of whether the planet is a round body that orbits the sun - it's been pretty well established that it's a round body. Whether it's orbiting a sun, though, or whether it has a tiny, hot sun orbiting it instead, is less clear. We can probably assume that it's orbiting a huge star unless we learn otherwise.