Q: Can I find out when my domain expires? Is there an easy way to find out which email accounts are associated with my domain?
A: Yes. There are many WHOIS lookup services online such as http://who.is that will let you find out the current status of your domain along with the contact email address of the domain administrator.
If you need to make changes to your domain registration account (eg. moving your website to a new server, renewing your domain registration, updating your credit card details etc. ) you must have access to the domain administrator email account on record with your registrar.