Any good exercises to increase picking speed, finger speed, and dexterity?
Start slowly, and gradually speed up.

I garuntee alot of people will say that.

But it's the best way, just play around with Chromatic scales *Good, if not - the best for getting all 4 fingers going* slowly and get faster.
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try playing the chromatic scale up and down each fret position making sure to pick each individual note, also don't use distortion, its kinda cheating you make more mistakes than you realize.
play anything, now play it faster, now faster still


Using a metranome helps aswell, increase by 2-5 bpm until you cant do it anymore

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trills(hammer on pull off) between all your fingers with the metronome

He said picking speed!

Anyway, just play chromatics all over the fretboard. Try string skipping every now and then too.
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Play ALL you know using only up strokes, for at least 30 min a day. After a month you'll be a lot faster.

That's not a bad idea. Thanks