A corp HQ can hold 5 divisions. (10 command points, 2 cp's per division) If you need more command, then bring it along to Sicily and give them something to fight. Otherwise, just leave it in Africa to await withdrawal.
Divisional paratroopers will always win against an empty hex. And they never drift. Broken down into regiments, they can/will drift...and if they lose a combat, will be destroyed. Mastering the art of paradrop is a very useful skill to have.
After a drop, paratroopers will automatically generate interdiction in their own hex and surrounding hexes...which means they could potentially deal out a lot of damage to enemy units that just walk up to them...even if the paratrooper dies in a subsequent combat. They will also block german units from reaching your beach.
In the initial Sicily landing, you don't really need to do the drop as the Germans aren't going to rush your beaches...unless you're Meklore. But he is just insane.
I find the best use for them is to drop them (a division) adjacent to an invasion hex, as they help the invasion combat, and give you a hex to advance inland. They can only drop within 8 hexes of a supplied hex (unit?) or to a hex adjacent to an invasion. (regardless of range, well..within range of the air transport)
“My logisticians are a humorless lot … they know if my campaign fails, they are the first ones I will slay.” – Alexander the Great