To get speed, first, you have to practice slow.

I use a technique often called "circular picking". I also use small, teardrop shaped picks. Whatever you use, try to only the very tip of the pick.

Attack the string at an angle, both up and down, instead of straight down/up. Make sure your shoulder, arm, wrist and hand are as relaxed as possible. Muscle tension will only tighten you up and your putting the brakes on.

If this kind of picking is new to you, exaggerate the circle, meaning big circles using your thumb and forfinger to control the pick (when I'm picking super fast, I notice my wrist often comes into play).

Over time, make the "circle" smaller and smaller, until the circle is shaped more like an ellipse (). The tighter it is, the more quickly you can return to the string, assuming you're doing a run on one string.

Economy picking: When you economy pick, you don't pick strictly up/down, up/down. So, say you're picking down and intend to go for the next string, instead of going over the next string only to come back up, simply continue down.

As far as fretting cleanly, again, practice scales and runs slowly. Very often fretting while picking fast gets sloppy because you're getting ahead of yourself, meaning your fretting and picking aren't in sync. You can "cheat" a bit by pulling off or hammering on, but I think you really should learn how to get both picking and fretting in sync.

If I get a chance, I'll comment on hybrid picking, but I'm hungry. :)

Oh, I like to practice picking on an acoustic. If you can get it down there, you'll be a speed demon on an electric.