She is near-sighted.
These are both grammatical and can refer to vision.
You should know that "short-sighted" has a second meaning, lacking foresight. For that reason, I prefer "near-sighted".
Adding person is not necessary and it makes the alternate meaning for "short-sighted" even more likely.
B. Both are OK. Person is not needed here either.
C. That's fine, or "an astigmatism". Many people, when they hear this word, think it is "a stigamatism". For that reason, I usually use the article "an" before it.
D. How many degrees near-sighted are you?
I am 30 degrees nearsighted.
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