What happens if I charge an enemy unit and it dies before the first close combat after the charge? Suppose they die from my magic phase. Do they get any additional movement or anything?
No, they do not get any additional movement.
What happens is the unit is not engaged in a combat, so it does nothing in the close combat phase.
I assume you are thiking of the Overrun rule? Where if you wipe out a unit in close combat on the turn you charge you get to move another 2D6" forward afterwards.
The rules for Overrun (8th Edition Rulebook, pg 58) specify that a unit only gets an Overrun if "all it's enemies have been wiped out as a result of the combat". So if the opposing unit was wiped out before the close combat phase began, they would get no Overrun move.