I rest ONLY my pinky on the body of the guitar for stability and it also makes it easy for me to mute my strings both for palm muting AND for keeping the strings im NOT playing with quiet.

Will an open hand or another technique make it easier to do such things?

ALSO will such "anchoring" make it more difficult to play live? standing up?

Is it easier to play standing up with a different technique?
Practice standing up. If you have never done it before, playing live will prove to be incredibally awkward.

Edit: Also, I don't think you can get any really good answers on anchoring. Alot of great guitarists do it, it's only bad for you if you put pressure? (I think)