Writing help...?

So there are probably better places to post this, but I don't really know where. Anyway, I'm writing a short story (not a screenplay, sorry) for a class, and I'm running into some POV issues... I wrote it in third person limited, following the main character closely, listening to his direct thoughts and having flashbacks. My professor suggested to try omniscient to flesh out the other characters a bit more and weave in more of their backstory. She got the sense that it was part of a larger work, and needed tweaking to stand on its own. Can omniscient third person include direct thoughts? How many characters' minds can we be in without head hopping?

The final draft is due May 10th, next Wednesday. It's only 6 pages right now, but she said I could go as long as I want to.

EDIT: Well, I passed it in last night. Still open to clarification on omniscient vs head hopping, however.