If by 'form of store' you mean the official Apple store; yes. I've never purchased a single thing from Apple's 'app store' (and don't really plan to). Everything I've needed so far is free.

The identity part? I have an account, so yes, some sort of 'identity' is revealed, but that doesn't relate to the credit card part.

They still do not know a thing about any of my credit cards, from initial setup to everyday use.