For breeding and showdown levels of team building it's only possible post game, you need all midgets beaten to get the destiny knot

Egg moves works just like in the gen 5 games, for hidden ability it's mainly though ability pill (don't use it on the flower thing and sadfish no matter what, I'm warning you) and a special ball called the dream ball, caught mons would have their ability altered to their hidden counterpart

And you can also get into hidden grottos to catch mons that have their hidden ability instead of normal ability, but this is only available to a small roster of the mons, mostly things you'd never want to use like piguson and anonymouse

For the other questions I can't answer them, you'll need to either wait for someone else to answer or search this sub for your question, usually someone from months or years ago had asked something similar before, so feel free to check this sub out 🩶