Shiny yes!

Lucky, I don’t think so - AFAIK lucky doesn’t exist in any other Pokémon games so there’s no point really in tracking it.

I believe the event costumes and a couple other PoGo specific variations cannot transfer as well, but most stuff can. You could pack Pokémon into your Switch games if you don’t wanna pay for expanded Home storage

I initially had a hard time getting accepted anywhere - couldn’t find any instances with open registration and the first few places I applied just never responded. I ended up applying to like a half dozen in one go and two of them responded so now I have two accounts. Lol