"During the lesson we do exercises."
Translation:Podczas lekcji robimy ćwiczenia.
It would have to be "zadania" ('robić' takes Accusative), which I've just added.
Note that "zadania" will be rather maths, physics, chemistry etc. "ćwiczenia" can be this as well, but is likely to mean 'physical exercises'.
"na zajęciach" - sounds fine, added.
But "no" for "na zajęciu". In this meaning, "zajęcia" is plurale tantum, no singular word is used. Which makes it quite difficult to count the classes you have on a specific day... for example, two classes would technically be "dwoje zajęć" but that sounds quite absurd to me. Still, it's correct...