1 - you're correct to assume that they are functionally the same as Psychic & Ghost, respectively! The only difference is that Control types have an immunity to Psychic, rather than a resistance. I suspect that you encountered Joey's Rattata on Route 1 and that led to some confusion about type matchups. I'd check out your Pokedex once you get it - there is a new page that displays Innate abilities for each species you encounter. Rattata, for example, has Normalize.

2 - They do not get STAB, which is why those abilities exist. They functionally give you back STAB.

3 - Special mons will always be either Control or Possess type. You'll see plenty of them as the game progresses!