TRYING TO UNDERSTAND VECTOR CALUCLUS - please help?

There was a time when I could have helped you with this. It's the sort of thing I'm particularly good at. It's just been too many years (about 8) since I've studied vector calculus though and I know longer remember the definitions of those terms other than that they are different 3D interpretations of the derivative. I think your approach to thinking about their meaning in physics is sensible though. Good luck.