How can my IP-adress be used to send enormous quantities of e-mails?

If you didn’t send them, your server log in password has been hacked. Change it now.

"mmm … I’ve heard of ISP’s shutting down peoples Routers, I’ve never heard of a landlord being pulled into it

If you have a shared WiFi then it could be a few people who are using your shared WiFi connection.

Shared WiFi is not very safe! If I where you I would get a VPN solution so no-one in your shared WiFi can spy on you.

Your Router offers out DHCP IP addresses these IP addresses are setup on a lease (a limited time) so the given IP address might have been with someone else and their lease expired and they didn’t re-connected so the lease was free then you came onto the scene and you snagged that IP address so you got caught holding the bag!

The other possibly here is your system has been infected with a Malware Bot! This allows someone to remotely access your system to send out Denial of Service pings or email.

So you’ll need to disconnect your system(s) from the WiFi until you can get a good antivirus program to clean your system or get someone to help you sanitize your system."