About anchoring your hand, just do whatever is comfortable. I usually anchor my and, not muting the strings, just anchor it when I'm playing fast, some people like to float the hand, whatever is comfortable.

Your PICKING MOTION should be the same, hand position doesn't matter, just the motion. You should be doing the same thing fast as you can slow.

Practice just tremolo'ing on one note on one string and just try going fast and then slow down and then go fast and then slow down, make sure your MOTION is the same.