Should I anchor my picking hand?
Ultimately, try not to anchor. If you can train yourself to keep your picking had off the bridge and body of the guitar, it will really free you up. Your picking hand should be loose, and anchoring does the opposite.
What pick is best for tremolo picking?
For lots of tremolo picking across multiple strings, you want something with plenty of give, a medium pointy tip, and a large thumb hold, probably with a grip (goat blood makes things slippery). For maximum blaspheming, I recommend a Dunlop Nylon 1.0mm.