I have some more questions:
Only emperors can create kingdoms and only kings can create duchies? Or a powerful enough duke/count can create a kingdom/duchy?
You need to be a duke with at least two duchies to create a new kingdom, and of course own/control enough of the de jure land (this is true for both duke and king titles). Usurping works as usual for both (claim needed, weak or strong depending on the situation)
If I create a duchy and give it to a count who is a direct vassal of (let's say) the king of Sicily (who's my vassal), the duke would still be a direct vassal of the king of Sicily? And what happens if I give him a kingdom instead of a duchy?
It seems they will become your direct vassals, but to prevent an angry king of Sicily you can (and should imho) just transfer the new duke back to him. If you make him king, all of his land will be de facto part of his new king title - this will cause some anger between the two kings. Also, I think he needs to be at least a duke to grant him a king title.
I have usurped the kingdom of France and the kingdom of Aquitaine, if I give the titles away would those kingdoms become independents or would they be my vassals?
Independent if you are a king yourself, vassals if you are a emporer. But very rebellious vassals if you are not the de jure liege.