What's your question?
Fixing mail? That needs a static IP and proper DNS on the public address, or the outbound mail will be treated as spam. It's possible to use a mail relay and there are vendors that offer that service, if you don't have a static IP address.
Running OS X Server not on a static IP? That won't work. Though you can run a static IP on a private network behind NAT and use a dynamic IP on a gateway-firewall widget. But that means outbound mail gets, well, somewhat messy. Unless you relay.
Or wiping and installing OS X client on the box? Yeah; there are discussions of that, and AFAIK it works. Whether it's considered supported by Apple, I don't know.
Or maybe what to use as a NAT gateway? There are various commercial packages, or you can run open source DD-WRT or OpenWRT or various other packages.
Or host the mail and related stuff "elsewhere" and get out of the hardware business. That's likely cheaper than a static IP on a monthly basis, and there are various providers that'll deal with mail and web services and such for you...
The slot-loader DVD drives can sometimes be flaky, yes. I know of several slow-loading optical drives that don't work all that well, or at all. (Well, optical drives start somewhat flaky, even when they're working. There's a reason Apple is getting rid of them in the newer systems, after all.) An external USB drive is an option, if you have one of those around. I'm guessing you're not looking to purchase a new Mac Mini box, nor to have the existing box repaired.
So which way are you headed, here?