1, 2, and 4) Yes, that's already possible. Look into Solo Keys for open source hardware and firmware. The standard allows for key manufacturer attestation but seems like the way it is going (especially with the proliferation of software authenticators) it likely won't be relevant in practice. You can also enroll many authenticators to the same account (provided the service allows it, which most do).

3) This is pretty hard/impossible, I think. The authenticators don't use the same key-pair for all websites (a la SSH through Yubikey), but rather create a per-service, per-credential key-pair, and encrypt it with the main key-pair. The encrypted credential key-pair is then handed off to the server for storage, and the service sends it back for the authenticator to decrypt and use during a challenge. Clever trick to not depend on local hardware memory and be able to have unlimited per-credential key-pairs, but afaik prevents you from just "adding lists of public keys".

I'm also not mentioning the resident keys aspect of the standard but that won't fix it as they're still service and credential based.