Sparta has much worse problems than war. Not to mention, even today some "spartans" don't consider themselves to be greek. It'd be like going to an icecream shop and buying a single cookie.
For the first two groups, public displays of intelligence suffices as a way to get a more comfortable life. For the last, tough luck - better try traveling to the future instead.
It's shit. The fun in dreaming is in experiencing the absurd, that's why I don't change my dreams even when I'm aware it's a dream (unless there's a particularly good oportunity to do so).
If you're going back to before technology got good anyway, might as well always travel to ancient greece (preferably Athens, as they're a bit less violent).
Generally, same. It's also competent (not good) at boilerplate.