What does a product need to do in order to be a base class for a ZClass?

It needs contain a class that is registered as a base class in the product's __init__.py "initialize()" method via "context.registerBaseClass()" e.g. context.registerBaseClass(ZCatalog.ZCatalog) See lib/python/Products/ZCatalog/__init__.py for an example...

Can another Zclass act as a base class for a ZClass? If not, why not?

Yep. Try it. :-)