Learn Russian: Он получил хорошую отметку.

The perfective получил focuses on the result of a single, completed action—he received the mark and now he has it. If you used the imperfective получал, it would change the meaning to a repeated action in the past: "He used to get good marks."

Could I use оценка instead of отметка here?

Yes, they are essentially interchangeable when talking about school grades. Оценка is generally more common and also translates to "evaluation" or "assessment" in a broader sense. Отметка is slightly more specific and literally refers to a physical "mark" written in a grade book or on a test.

Why doesn't Russian use a verb like "make" for getting a good grade?

In English, it's common to say "I made an A," but Russian handles this more literally. Because the teacher gives the grade and you are the recipient, you always use the verb получить (to receive/get).

Just as a quick refresher, why do the endings change to -ую and -у in хорошую отметку?