Yes, the whole point of using client side certificates is to enable you to reliably uniquely identify each client.
AWS will provide APIs to provision each device with it's own cert/key.
The other reason is that it means that you can easily ban a single device if the certificate is compromised, if every device reuses the same certificate then you have to ...
I think most locks will offer option number 1.
For 2: The Schlage locks state this Built-in alarm technology senses potential security breaches at the lock, while the low battery indicator offers advanced warning for battery replacement
Also I found August has the following alerts:
The Door is locked or unlocked manually
This alert notifies you when someone ...