While plagiarism is a recurrent problem, the main purpose of references to the scholarly literature is to indicate your being in touch with that literature. Definitions and notions are sophisticated, and it is likely that even an authoritative dictionary won't settle the meaning of terms in scholarly discourse. (My favorite example is the use of "collaboration" as in collaborative planning. Used in that context, its meaning is clear. But all I can think of is Nazi collaborators, highlighted for me by the famous Robert Capa photograph of an alleged French collaborator after WWII, her hair cut off. I should note there is now some criticism of these photograph and what was done. There are many such photographs.)
Critical thinking skills mean that you not only know how to make an argument, but you indicate you are aware of the problems with your argument. That may be explicit, it may be in notes. You know that history is likely to be presented with a certain bias (but professional historians readily acknowledge their orientations, and that is part of their argument), so that simple stories of progress are surely nonsense. You know that an argument that has an uncritical or unscholarly section is likely to fall apart no matter how strong are the other parts.
Moreover, in scholarship and in critical thinking the idea that one might quantify everything, or most things, is generally thought to be a mistake. Judgments can be justified, but not always or often quantified. On the other hand, Kahneman's Thinking Fast and Thinking Slow points out how often quantified judgments might well be powerful, but what is then quantified is very different than what most people pay attention to. (Think of the movie Moneyball.) Clinical judgments might well be replaced by statistical tests, the diagnosing psychologist by an Minnesota Multiphasic Personality Inventory (MMPI) or its more recent successors.
One of the most interesting phenomena these days are automatic grading of essay questions, and the correspondence of those grades with those of readers of the essays. What you need to attend to are the poorly corresponding cases, to find out if you are missing important stuff: very poor essays that pass, and excellent essays that are missed.
More generally, you want to ask;
Who says? Who disagrees? Why?
Are there interesting analogies with other cases?
What are the specific meanings of notions in this field or discipline?
Here is what I wrote to one student:
There are two features of doctoral work that distinguish it from work done earlier in one's education:
a. Reference to and acknowledgement of the scholarly literature. In other words, when you write a paper, you must deal with those who support your position and those who do not, and in particular you must be fair to all of them. By "fair" I mean that you have to represent their positions adequately, and deal with their support and objections to your own position. You may have strong feelings and an articulated position, but you must be able to deal then and there with objections.
b. You must think critically. This is a bit more general than a. Namely, you want to be twice as critical of your own position, so that you can be able to see its flaws and indicate how you might deal with them.
Most popular writing on a position may present strong arguments, but usually it does not deal adequately with the scholarly literature and often is much less critical than it is advocacy.
When you want to write a rationale for changing public policy, you would need to deal with the current orthodoxy and why it might make sense. On the other hand, were you being an advocate with no claims to scholarship, you will surely leave gaping holes in your argument but also be much more emotionally convincing.
As for procedures: If you have a problem with a course, your first recourse is to see the instructor. The university rules say that administrators come in afterward, if you are not satisfied with the resolution. Students should be empowered to deal directly with their instructors. (Of course, you are welcome to seek counsel from whoever you wish.) I don't want you to give up a proactive stance.