Re: There is/are no student(s) in the classroom
We often SAY (not write) "There's... " for a plural. Only the contracted form, not "There is."
There's a few things we can do here.
But your original sentence will be more natual with the plural: there are no students. We rarely say "there is no [single thing]" to mean that the room is empty.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.