There is no 'right' way to pick. The right way is the way you find comfortable and that allows you to do what you need to do. The only important thing to remember is to relax.... as stated above, speed comes from solid technique rather than gritted teeth.

Keep in mind that much of S.O.A.D's music is tremolo picked, which is a little different - that's just going as fast as you can but without caring how many times you play a note. Strict alternate picking is more difficult than this.

Most fast pickers (Batio, Petrucci etc) use a combination of wrist and forearm depending on what they are doing. I also use a combination of both. When skipping between strings I do find myself using little circular motions as well as the straight 'up, down'. The way I pick changes with what or how I'm playing. I learned to do it the way that worked for me.

I float my hand over the bridge and don't anchor on anything. I'm not the fastest player in the world, but I do OK.... :D

George Lynch is a weird guitar player. Strange style, strange scale choices (or some of his own invention) and very wide intervals. As with everything - you're not going to play it fast if you can't play it slow. Work it up over time and remember that it isn't a race. Spending extra time at this stage will save you having to relearn picking technique later....