"She is a student."
Translation:Sie ist Schülerin.
Both "Sie ist Schülerin" and "Sie ist Studentin" are fine. Note that they're not interchangeable.
Also, it sounds more natural without the indefinite article.
If "student" and "pupil" are not interchangeable, Duolingo shouldn't suggest that they are, but it does.
When can we drop the article? I wrote "Sie ist eine Schuelerin" but it also says "Sie ist Schuelerin" is acceptable -- which is more natural and what is the rule for omitting the article?
German here: Both of these options are just fine, but with the article it is a little bit more formal. But just a little bit; no one in Germany will care which you choose. Most Germans usually go with " 'ne", which is the short form of "eine".
I don't think there actually is a rule for when to omit the article or not, but I may be wrong here.
"Sie ist ein Schüler" would also be grammaticly correct, despite the wrong gender. It is common to refer to females in the male form, at least in the everyday language.