1)
Evan\'s book, pg. 415:
Also, the critical aspects of the domain model may span multiple Bounded Contexts, but by definition these distinc
1a) Yes, the Core Domain essentially is the set of bounded contexts that worth the application's development from the customer point of view.
1b) No, some generic elements often play a key role in the Core Domain. See for example Time, Currency and Money that are present in many Shared Kernel: they are really generic but important to the Core Domain rules.
1c) Context boundaries are defined after terms' semantics. In a BC, no term should mean more than one thing (see also SRP). They are almost linguistic boundaries! When you see that a class has more than one meaning in the domain expert's mind, you know that you have mixed different BC.
2) Yes, Generic Subdomains are those part of the domain model (or, the set of the bounded contexts) that are useful but not central in the application. I've built several applications with generic subdomains: when they add some value that the customer wish to pay (and I can't provide such value with a simple CRUD component).
Note that what's "Core Domain" in your application is a qualitative definition: I've seen many times secondary parts of successful applications to achieve importance when the customer's corporate organization changed. Thus, what is Core Domain today might be not tomorrow.