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
Do they stay shiny/lucky?
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