It's likely implemented as a part of the System-on-Chip that Apple is using in their phones, yes, either reusing or is very similar to ARM's TrustZone extensions.
Since the Apple chip is derived from an ARM design it would make sense to have the secure enclave implemented with TrustZone rather than being provided as a separate piece of hardware. Most probably a TEE (Trusted Execution Environment). Lots of TEEs are based on L4.
Nope, it's a separate core, according to Apple.
Educated guess: it may be the application processor also has a trusted execution environment containing stubs that communicate with the Secure Enclave. This would prevent kernel level exploits from writing to the shared memory and mailboxes.