Can you set-up sub-domains like abc.ymydomain.com?

Yes, not a problem.

What happens after the expiry of a domain name?

The domain actually expires and someone would need to pay for another year (or more depending on the domain name ending) domain name registration. It is a little bit like your car registration, it needs to be renewed every year.

Who owns the Domain Name you register for me?

The domain name you register with us will be fully registered in your name and you will have complete 'ownership' or authority over the domain. The only thing we set-up is the domain name servers to ensure your domain name is hosted/parked on our server.