Gmail – Which Gmail domain names are available

At present, it's pretty much anything that accesses your Google account and doesn't go through the web interface -- chat clients, email clients, etc. You'll need a different password for each one -- they're one-time passwords ¹.

When the domain name expires so will the MX records for that domain. As you have already verified the domain with Google theoritically you will still be able to send email as that domain (since you are using Google servers to send) however you will no longer recieve incoming mail.

Its possible that Google might detect the domain is no longer registered and prevent you from sending mail.

That being said, Google wont disable or delete your apps account when your domain expires (provided you continue to pay the subscription) - all your data will remain and the account will still function, just without email (eg. you will still be able to use your Google docs)