Can students ask for changing grades?
A student sure can ask for re-grading, but he or she should have strong evidence that what was graded was better than perceived by the grader. It is a very bad idea to try argue how the teacher should be grading (e.g., asking her or him to grade according to what work you claimed you provided rather than the quality of your homework or exam). These questions are up to the teaching teams, not up to the students, and yes that makes the situation rather unbalanced. What you can do about this is to ask for a general change in suitable meetings if they exist.

Moreover, I would like to point out two things :


most of the time, grading is not for acknowledging good effort, but to measure if the student understood enough of the class to have a decent chance in the next one (at least in fields where classes depend strongly one on another, like in mathematics);
my experience tells me that students that consider they understand well but do poor exams in fact understand much more shallowly than they think, and their grades should be taken as an indication that the way they work is probably not good enough.