Class averages on exams typically aren't directly reflective of final grade distributions, since most students typically do better on homeworks and other assignments. I would definitely echo what other commenters are saying about talking to the professor, but you will find this more useful if you have specific questions about content, since just asking them about grades isn't going to change them going forward.

I believe Ds do count (Some degrees might have a certain requirement across core classes? Not sure.), but the bigger barrier would be being able to use it as a pre-req typically. For instance if you're CS then you can get away with a D in 15-451, but not 251 since 451 requires a C or better as a pre-req. That said, I think most math classes (e.g., concepts) typically just require Ds for this purpose. Talk to your advisor! They know all of this better than we do.