Gateway/router

Possible? Sure.

Generally painful to set up, comparatively difficult to secure (particularly given most folks are incessantly making software changes right on the gateway box, which can open up remote-accessible ports), expensive and slow as gateway-routers go (general-purpose boxes and operating systems aren't good at slinging packets around) and generally a networking configuration with a very rich history of questions here in the forum, too.

Do you really, really want to do this stuff with your Mac Mini Server box — the hard way — or would using another device — ranging from an AirPort Express to a spare dual-NIC x86-class box with some open-source gateway-firewall software loaded, to a more advanced gateway-router device with VPN server capabilities or related features — better meet your requirements?

If you really, really want to do this the hard way, then enable Internet Sharing in Internet Preferences in Mountain Lion, and launch Terminal.app from Applications > Utilities and start reading up on man pfctl and related information. The NAT service is not managed via Server.app. Use of the NAT service will conflict with any sort of customized DHCP, too. (And down the rabbit-hole the configuration goes...)

As should be obvious, I am not a proponent of using OS X boxes as expensive and comparatively clumsy gateway-router devices. I'd get an external, dedicated box that does NAT (and possibly VPN services, if you need remote access), and configure that as your gateway router box.

I prefer to use a dedicated box for VPN services as that avoids having to pass the VPN through NAT.

Multiple L2TP sessions tend to get tangled and fail when passing through a NAT device, too.

I generally use OS X Server for DNS services.

DHCP is usually on OS X Server, but there are cases where there are multiple (coordinated) DHCP servers operating on the same subnet. One that I manage has three (coordinated) DHCP servers operating on the same subnet, and works just fine.

I'm presently testing with a ZyXEL USG series gateway-firewall-router box. It's a fairly complex box when you first start using it and definitely presumes a familiarity with IP networking, but I'm finding it has a relatively sane user interface as these devices go. I've not yet verified the compatibility of the VPN services with the box; that's the last major test pending. (I do have some DNS resolution capabilities configured in the ZyXEL, though strictly as a tertiary backup for the main DNS servers.) For open-source, there are folks around that recommend the pfSense firewall. M0n0wall and Smoothwall are two other open-source choices that get discussed. If you want to try using OS X or OS X Server (again) here, have a look at IceFloor.

As I usually suggest for these... Access or download the manuals for the device and see if you can figure the device out from those, as that's going to be what you'll be reading through in any case...

Skim the OS X Server manuals?

Your particular expectations and requirements are another factor.

Using a server as a gateway-router-NAT box is not something that I'd recommend in general, and that's irrespective of the operating system involved. Dedicated boxes tend to do that better in my experience, and the prices on those boxes are continuing to drop, and as both commercial and open-source becomes more capable and easier to use.

While it's certainly possible, trying to have one box do everything leads to complexity and compromises.