Hey Sesame! The correct is "We'll have no class on the next session", assuming that you normally have one class each session. If you say: "We'll have no classes on the next session", you are saying that normally you have classes (more than one) in your session, but on the next, you will have no one. But, if you have only one class each session, and on the next time you will not have any, then you can say that there will be no session at all. In case of you are gonna have the session even with no class, just a free activity for example, then it becomes acceptable again. I hope this helps!

Yes your logic is correct, it should be the singular form because it is only one class session. If you say "classes" it will refer to multiple sessions or multiple classes (subjects). For example: "Next week there is a holiday, so there will be no classes held next week."

Hi Sesame, you're correct, it is 'we have no CLASS next session'. I understand the impulse to use 'classes' as in Spanish, we often say 'no tenemos CLASES la proxima sesión.' This works in other languages, but in English it will just sound confusing to pluralize. Cheers!