I would argue that "ocena" includes "evaluation" as well as "grade".
Yes, I would also add "assessment."
In any case does this mean "grade"as in a mark on an assignment but not grade (US usage) as in year in school (first grade, second grade, etc.)?
Yes indeed, a mark.
'What are your grades?' is presumably wrong because it should be singular?
Yes. But we changed the main interpretation of this sentence to "What is your assessment?" (what is your view, your opinion), because as a question about your grade, it sounds rather clunky. But if it was, then it's just a singular grade.
"How is your grade?"
grade versus result