Is it grammatically correct to say "Un prof enseigne les/des élèves"?

Answer 1

No.

Choose either les or des.

Answer 2

Yes, but is either of them correct?

Answer 3

Yes. If you have a particular group of students in mind, use "les." If you mean students in general, use "des."

Answer 4

"Un prof enseigne à ces élèves" is better