Is it possible to show a module with AMM on a Zoo item only within a category, and not on every single instance of that component under a menu item? In other words, if I have a menu choice called "Residents", which is my Zoo app instance of a Documentation, and 2 categories underneath that, "Homeowners" and "Renters", let us say I have an item in Homeowners called "Single family dwellings" that I want a module to appear on, but in none of the other items or categories. Is this possible with AMM?

You could control that via the php field to check for whatever you want. You just need to know the php code necessary to check for the data you want...