Short introduction: we want to separate our application to 3 editions, and one of them will have triggers and some specific pages, and another editions - no, so with such structure we cannot use one common application with some flag, that would identify the desired edition and change functionality (we don't want to add needless elements to package at all).

a) is it necessary to have 3 managed packages in our case? Or there is a better way?

b) and can we use one core(several Apex-classes) for different installed applications? Let's say user already has installed App_1, is it possible to install App_2, that will use some part of App_1's classes? Without creating new classes - duplicates(that will only have another namespace prefix).