My only comment is on Seiuchin kata. While you are in the straddle stance, you withdraw your front foot slightly before doing the stepthrough with the rear foot. I have always been taught that the stance is set and the rear foot glides through into the next stance without drawing the front foot back. Again, styles/dojos vary and I wasn't sure if this is the way it was shown or not.
I meant to mention that, thanks. Yes, we do it as I am doing it, I'm pretty sure I'm doing it 'correctly' for our dojo. When we start training a student in Seuinchin kata, they pivot of the forward foot, basically just turning on that foot 180 degrees to face the other way. Later, our instructors show us that this eats up distance but it also pivots us into our imaginary next opponent; like 'here I am, please punch me now'. So, we 'halve the distance' intentionally by moving both feet. I am not sure if there is any distinction made between which foot moves first, but I can ask in the dojo. Often, on questions like that, our main sensei will say
"Just get it there," meaning it's not important to the kata as long as the move is completed smoothly and balance and speed are kept. He's a very careful person, sensitive to the lineage we are taught by Masters Mitchum and Harrill, but in some little aspects, he doesn't seem to have a preference, or in some cases he has said
"I asked Sensei (Mitchum or the late Master Harrill) and he told me, etc, etc." I think that foot movement is one of those; he doesn't much care how we get there as long as we get there.
That same movement also comes into play during Wansu, when turning to face the first opponent with a chop block followed by a (blocked) kick (the knee-fake kick). In fact, I bobbled it in the Wansu video above; the turn is supposed to keep you both on the embusen and move you back slightly so that you do not turn directly into the attacker's attack. Same foot move; but again, sensei says he doesn't care how we do it, just that we do it and don't wheel about on one foot (getting off the fight line) or step in while turning and get punched in the face while preparing the chop block.
So you could say I'm working on it; but yes, we do it like that - or at least I do and I don't think Sensei cares one way or the other. I may ask him though, thanks.