The under is not accessible.
Yes you can rebattle Mirror B anytime.
There are "wild" random encouters thanks to the Poké spots and the poké snacks.
As for the rest, that's up to Stars to answer.
But I'm just gonna say that you're asking a LOT to someone that is working alone, during his free time, while he doesn't get paid (he deserves the donations guys, a new game costs around $60 atm, and I'm sure you guys have had more fun with this game than other recent game, so please consider it!) and that has some limitations because it's a patch of the original game.