Are any of those skills part of your system ? If so, what do you call them and what methods did you use to develop them.
I would call the kinds of things you are describing "Kokyu". We use stability drills to train this sort of thing. Lot's of having a person stand still while we push on them. I do this quite a bit with my kids class, it's really good for them. I've noticed that I don't teach/practice it so much with the adults anymore. I believe this is because if they are training the forms correctly, and asking the right questions of themselves, they will naturally figure these things out. I do however use these kinds of practices when I have a student who is naturally unable to develop this kind of power.