"There are few students in this school."
Translation:В этой школе мало учеников.
Yes, "a few" and "few" have slightly different meanings. It's explained well here: http://english.stackexchange.com/questions/1866/a-few-vs-few
The difference is similar in Russian. Also несколько would probably be even better translated as "several"
студент is an undergraduate (likely, late teens and older). Ученик studies at a school.
We also use ученик as a general term for a student of some "teacher" (e.g., an artist, a philosopher or a prominent scientist who left followers). Студент, on the other hand, usually attends a college-level organisation or a private school for adults.
Высшая школа экономики is a university, not a school. When referring to an educational institution, школа is not a generic term: it only refers to where schoolkids go.
Unless it is used as a part of the institution's name, of course. ВШЭ is as much of a school as a guinea pig is a pig. Names are sometimes deceiving. For example, Moscow State Linguistic University is, arguably, not a linguistic university—at least, not primarily (linguistics is not what it is or historically was focused on) but rather a language university, i.e. the one that teaches translators, interpreters and language teachers (and also linguists, lawyers, psychologists).
There is, however, one context where this truly works: when a "school" is not your average school for children but a company that provides classes that teach certain skills (e.g. "animation school", "fencing school"). Using ученик in this case is odd.