Night classes
You may train students at any time if your licences and rating allow. Opinion is irrelevant. Although some exercises such as PFLs are limited at night, aren't they.
Ex3 is 'air experience' and may take any form that you wish. The first thing that a prospective student and the instructor need to know is; how do I cope and do I like being airborne in an aircraft and do I wish to learn. An important element prior to commencing with EX4 -19. Most likely you will introduce tiny bits of most elements of flight. Many people will find it a very special experience being airborne at night.
Horizons do not disappear simply because its dark. Horizons disappear at all times.
IFR/VFR makes no difference. AOC's can contain anything but are related to the specific operations. IFR does not determine how many engines that you must have.