How is e-mai being sent from an account that doesn't exist?

Spam senders and scammers use email addresses they get from lists captured from infected machines. So if a spyware or virus infection gains access to a computer it can send the originator a list of all the contacts on that machine. Also if you ever gave that address on a site as contact information, and the site is at all dubious (often sites providing pirated software, even if you just sign in but never download) sell on such information. Totally illegal, but that is how some sites earn their money. So the people who buy them use every email address in the list to send to, and also every address in it to send from.

In theory, when you send an email it MUST go to your own email server, and is verified by your password before it can be sent. If it goes to any other server that server would reject is as being from an unknown user. Unfortunately there are always some severs run by useless administrators which are not correctly secured. So the spammers send emails addresses to themselves to mail servers everywhere and if they receive the email back they know they have found an unsecured server. Any they find they use to end thousands of mails from and to every address they have collected. That can take about 2 minutes. The server they use will be blacklisted within 2 days as an open spam relay, but the damage is done and the spammers go elsewhere.

So they must have gained your fathers address from the same infected machine they found yours. A common contact.

I see attempts to spam through mail servers I manage hundreds or even thousands of times a day. The get bounced so each spammer knows they can not use it. But there are a LOT of criminals out there.

I can send an email from any address I just made up, or even your email address, to any address I want anytime. It requires no hacking skills. The ability to do so has been around since email was invented back min then 70's.

Automated apps are available to send fake email form your phone. the same is true for sms.

Fake web sites are trivial as well,

just take a basic internet course.

It's called Email Spoofing, and commonly used by spammers and other malicious scam artists. http://en.wikipedia.org/wiki/Email_spoofing

Good Luck.