"Lauf du vor, ich komme hinterher,"?
Why is there 'du' between 'Lauf' and 'vor'? Is this an imperative sentence?
yep, it's imperative. I don't think the "du" really has to be there.
"Du" is there to stress the contrast between you and I. The sentence would also work without "du".
Yes, it's imperative.
The du is to emphasise that the command is addressed to du (and not anyone else); here, specifically, to set up a contrast between what du is supposed to do and what ich is going to do.
In English, it would be, "You run ahead; I'll follow behind" with explicit "you" before the imperative.