SolidState

FRLG, Emerald, and GSC should work as expected. Which is to say, Emerald's still broken for soft resetting of course. Ruby and Sapphire should work as normal provided the flashcart has a real time clock, which both the EZFlash Omega and DE do. RNG manipulation still works as normal in my experience.

It depends on how they're transferred. Pokemon made via an emulator are legal as long as you're able to get them onto your main games undetectably. Using a homebrew program like Checkpoint to put the save file on an actual console or cartridge won't raise any red flags with Bank or Home, assuming you didn't cheat in some way. I would be wary about using some third party service to move the Pokemon over as you never know what their procedure is and if it would possibly flag the Pokemon as illegal.

Yes, max contest stats can be legal as far back as Gen 3. Getting perfect stats in Gen 3 is extremely tedious and I believe it requires the use of eReader berries, but it is definitely possible through official means. Sheen was ignored when feeding Pokeblocks in ORAS making maxing out any Pokemon passing through Gen 6 very easy. I think it can still be done in BDSP but requires making very good Poffins in Amity Square. Linneus's The Absurd Depths of the Pokeblock and subsequent Poffin video are full of information about this if you want to know more.