I actually was going to point out Parallels as case and point, but I managed to forget too, lol.
I've always accepted the Mirror Universe as different quantum universes, honestly.
As for warp, based on Einstein's theory and most other theories I am familiar and as far as I understand them (and by no stretch of the imagination am I physicists or even aspiring one), I've always understood that faster then light travel is possible but the amount of energy required pushes it into the "unfeasible" range. I've always just taken as a forgone conclusion that Star Trek has overcome this. Not to mention a recent article I read (I forgot where at this point) suggested there may be a great shortcut to warp travel making it more viable then space folding again.