이 seems to be short for
이것. Can a fluent speaker confirm please?
I mentioned on another post, but 이, 그, and 저 all stand by themselves respectively as "this", "the/that," and "that (over there)." Likewise 것 stands alone as "thing." You'll see 이 그 and 저 used before any noun.
"That student" is wrong, in this case?
Yes. "that student" would be 그 학생
- 그 학생 if the student near the listener (away from speaker)
- 저 학생 if the student away from both speaker and listener.
- 그 학생 if the student near listener (away from speaker)
- 저 학생 if the student away from both listener and speaker
True, 이 학생 would be this student.