Overall, a pretty decent post with mostly correct information and you`re getting really close on the other points. You have mostly correct ideas here but you're not quite there and have a few misconceptions.
One big one is that no you don't need to point the board down the hill to make an edge change. In fact, on steep terrain, you want early edge change with the board across the fall line so you can work the top of the turn. What the board has to be doing to make any safe edge change is be traveling straight tip to tail with no sideslip. The board does not care what direction it is pointing.
I think you are trying to describe board performance concepts which are actually Tilt, Twist, Pivot and Pressure. I am assuming when you say "rock" you are referring to tilt. As for twist, you should not be using any twist if you are truly carving; this is all about tilt.
If you are doing a dynamic skidded turn, twist is certainly not for just the initiation of the turn; you maintain twist throughout the entire turn.
So, we use different board performance concepts depending on the type of turn we want to perform.
Not dissing you or trashing your info, just adding a little bit of higher level information to the already good grasp you have here......cheers...