#1
Mostly downpicking, I can't even downpick fast enough to play the fast riff in Seek and Destroy.
...I like metal.
#2
Just practice anything. Start off slowly and work faster and faster. The easy scales help. Chromatic, penatonic, etc.
MY GEAR:
PRS SE Custom 24
Jackson DKA7
Gibson Explorer
MESA/Boogie Express 5:25
BOSS GT-100

BOSS TU-2
Dunlop Cry Baby Classic
BOSS NS-2
VOX Joe Satriani Ice 9 OD Pedal
VOX Joe Satriani Time Machine Delay Pedal
Ernie Ball Strings
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#3
In my experience, you can train to play alot faster for brief periods of time, or you can train to play at a certain speed for an extended period of time.

When I was learning metallica's One, I first developed what I would describe as power in my picking so that I would play alot faster than normal for a short amount of time. This worked great since, after some days of practicing, I was able to roughly execute at least three sets of the 16th note triplets in the song (i.e, what they play when saying "Darkness, imprisoning me, all that I see..."). However, I had to develop endurance in order to play through the song after "Left me with life in hell..."

Basically, it's like powerlifting. You visualize what you want to do, and then prepare yourself to do it. I would literally stare at the fretboard and visualize playing the notes, wait for it to "click" in my mind, and then started playing. It was stop and go at first, but that quickly changed and then I was able to play those notes at the appropriate speed. I also used a metronome to practice the same sixteenth note triplets over and over, basically building up my focus and then jumping into the notes. Once I was able to play the riff cleanly, I then moved onto developing my stamina.

I used the above approach to increase my maximum speed of execution, and then I just kept playing along with the song as long as I could until I was able to play through the entire thing. That's how I developed stamina, and it's really the only way to do it.