Is it unethical or illegal to grade a proof exam without reading all of the proofs? Someone I know would give students 0 points if they do not use theorems presented in lectures, or if they have one solution that solves multiple problems at once will ignore it. Also would make up criteria to fit his/her own agenda for punishing students. Then he/she would leave it up to the students to possibly argue for changes in office hours. Is there some standard criteria for grading proofs, either on a legal or professional level?
Based strictly on the information you have provided to me about this mystery person, I'd say the instructor engaging in these activities is highly unethical and may have some other psychological issues. That's just what I sense "prima facie". "Absolute power corrupts absolutely", but I could easily be wrong.
Then again, maybe the mystery person has explained the grading criteria, but hasn't explained it clearly enough.
Be very careful about making a formal accusation against this person. If you make an accusation, make sure it's iron-clad and infallible so that you're certain to win.
Many years ago, in an Engineering Mechanics class, I openly accused my professor of erring in his solution to an exam question. My exam question was marked as "incorrect" with very little partial credit. I stared at that problem for some time and concluded my solution was correct and the professor's was wrong. I treaded very gingerly as I described my disagreement with his solution, but I went step by step and ultimately, before the entire class, he admitted he was wrong and I was right.
I was about 18 or 19 years old at the time. Trust me. Be very careful. Professors are smart and they don't like to be proven wrong. My professor was, thankfully, a person who loved truth more than being correct.
It is not necessarily wrong for a proof to be marked wrong without reading the whole thing. If it sets out to prove the wrong thing, it is wrong. If it starts at the conclusion and works towards the hypothesis (a very common mistake) it is wrong. If it assumes something incorrect, or simply not shown, that makes it easier to arrive at a proof, it is wrong for the purpose of the assessment. If it proves multiple things at once, it is almost certainly wrong, in such a context. If it is illegible it could get no marks regardless of other factors. If it is correct but hard to read, it may be worth no marks if that was the assessment criterion.
And, no, there is no universal mark scheme. For anything (at university level).