Yes you can do it on purpose consistently. You can do Blanka’s hop tricks or Sagat’s tiger knee crossover tricks to force dragon punches to come out the wrong way. Good Blanka players will always use his hop tricks to force characters animations to come out the wrong way and then go for easy punishes. I think Blanka’s hop can’t be thrown either, so you can even bait a reversal throw to animate the wrong way and then punish it.
Here’s two more cross up tricks. First one is the crazy legs trick where you pass through your opponent. Second one is Yaya doing tiger knee tricks to get his opponent’s dragon punch to come out facing away from him.
Edit: look at the start of the second round in the first match. Mattsun does a hurricane and gets over Makky7 causing his crouching fierce to come out the wrong away.
Numbers one, two, and three are wrong. You can get opposite attacks off of light attacks when they cross up. You can get opposite attacks is the opponent is standing or crouching, on both block and hit. Jump attack timing can vary widely.
Number four I have no idea if that is true or not. My guess is that it is not side specific though.