Actually that has nothing to do with speed. That's a "Matrix" affect that makes it look as if he's fast, when really it's just poorly edited cinematography.
2:38 to 2:42 is the opening bro. But again, that's really not out of speed but rather good timing on Dante's part.
No, that's called distance and good timing. Distance because the bullet was far enough from Dante for him to actually open his mouth, and the timing Dante has to open his mouth has nothing to do with speed, but instead the lucky timing of opening his mouth at that specific time.
That again, is called timing. Dante's not fast, but rather he seems to posses heightened senses that allows him to hear at march five and dodge it at the right time. Hell, Vergil probably isn't even that fast. All we have for Vergil is gameplay, but no actual cut scene shows that speed. unlike DmC Vergil, who we see can actually move that fast.
Dante isn't march 5 speed from what you've shown, but rather he has march 5 luck mentally, not physically.