1. Yes, Asterisk can register as a client to a different server.
2. Yes, you can script this in you dialplan. F.e. call a http url, insert specific info in a database, etc.
Mind you that the answer to question 1 is not specifically tied to the B2BUA functionality. B2BUA means that Asterisk will always be in the middle of the call, where a proxy like Kamailio (OpenSER) will just relay the request.