Those kind of missions have been moved to the "Explorer missions" or what they are named now. You can turn them on in the preferences window somewhere if I'm correct. They have been turned off your map by default.
You can't play any "class" missions on the character that has started KotFE (class missions = chapter 1 up till 3, RotHC and SoR).
You can of course still visit the old planets.
Difficult one. I'd love to be a Chiss, Togruta or Twi'lek. But what and where? Perhaps if I were human and born in the Empire, I'd be a Moff or something. In the Republic, idk really.