Is it right for a teacher to say to their students in class: "Now let's correct the exercises." Is "to correct" the right verb to use?
This is idiomatic.
It would mean that the teacher will tell the students the correct answer, and the students have to check that their work is correct and write the correct answer if it is not.
Sometimes when the teacher takes the students books to look at their work this is called "correcting" or "marking" the work.