Has to be on the same phase, can be on a different circuit though. You can test by plugging a light in at both points you'll be connecting to then switch the breaker in your meter box to see when/if both lights go out at the same time.

Should be fine as long as you're not hoping to stream HD video or anything. Your router handles all the DHCP stuff, so they're just plug and play.
+1 to buying from somewhere that has a return policy if you're not happy.