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... For each point by which the result exceeds the target unit's Leadership, the target unit suffers 1 wound with no armor saves allowed

My question is, do you use the unmodified leadership of the unit? Does the unit use it's general's leadership if he's within range? Is there a re-roll with the standard close by?

Yes, you can use the General's leadership if he is within range as the ability does not say "unmodified". As to using the BSB, you only can take a re-roll if it is a Leadership test. If it is just a roll that is compared to your Ld, then no, you may not re-roll. From what you posted, no, you may not re-roll.

I do not have my book nearby but that should cover it.

You can use the General's Ld, but not the BSB as its not a ld test.

You can't use the BSB's re-roll, because you aren't rolling any dice, your opponent is. The vampire player rolls the 2D6, adds remaining wounds, then compares to your Ld. Since you have not rolled dice, you cannot claim any sort of re-roll.

-Matt