#1
its proper technique to keep your alternate picking flowing even while changing strings, for example down up down, then when you go to a string below it you start on an up stroke which is sometimes difficult because you have to bring your pick up and around.

but when alternate picking at very high speeds this is insanely difficult. Does it take a ****load of practice or when playing at insane speeds to the laws of alternate picking just go out the window?
#2
I've always thought that Number 1 is to do whatever is comfortable without getting sloppy or slowing you down.
Otherwise get a metronome and start slow and go up once you're comfortable with that speed...
You'll get it eventually.
#3
Its really all preference. If you want strict alternate picking, I would keep it up/down regardless of strings, though if you want to do economy picking instead, thats fine too.

Sweeping is an entirely different thing, because that pretty much relies on the fact that you're picking in the same direction (i.e. down/down/down on the strings).
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