The crouch recover from a power hit is very useful. Just hold back when you get hit. If you don't do anything you'll stay grounded and your opponent can come in and has a chance for OKI. you have a better chance to defend yourself when you recover standing up.
The Chinese get up is simple. Just hold forward when you hit the ground. Mostly everyone can do this and I know Yoshi can. It's a little risky though, it's pretty slow recovery and if your opponent is waiting for you you're going to eat a launcher.
One other thing I want to point out is this new thing we call the "ass stun". There are some moves in T6 that doesn't launch like in the previous installments but just knocks you on your ass and it's a free launcher (G-clef is a perfect example). When you hit the ground just quickly roll to your side and you'll recover, otherwise it's a free juggle.
Nowadays I'm getting used how the top players I see on youtube recover. They roll to their belly first and then roll away from the opponent. I think it's safer than just rolling back regularly since it's slow and easy to see. I still use recover to Indian stance from grounded though. I can either gain health if people just stand there waiting for me or I do cannon when they come in. There's many ways to recover though so depending on the circumstance just do what you think is best.
And of course never forget the Phil players hehe. Gotta represent! I've played some amazingly good players when I visited Philippines early in the year. People only get better and it's only a matter of time. Even though Korean and Japanese are at the top, someday we'll rise to those levels too hehe.