Mac Mini has one ethernet port - can you split it for two different tasks?

There are three options.

1. You can define two (or more) different sets of IP addresses to run on the same physical network interface at the same time, I have used this to for example have one version set to DHCP, and another with a static IP whilst I am reconfiguring a router to change its IP address. Sometimes you have to first change the routers own IP address, let it reboot and then change its DHCP server range meaning that DHCP clients would initially have the wrong details hence using a static version. I don't feel this approach would be suitable for you.
2. You can also define multiple VLAN entries for your physical network interface this segregates traffic but lets the computer talk to both (or more) sections. This also I don't feel is suitable for you.
3. The final option is to get a USB Ethernet port adapter to add a second physical network interface. This would then give you effectively the same capabilities as your previous Mac. I would need to know the Mac mini model to suggest the best choice of USB adapter.

That's technically feasible, as is the ability to add a second Ethernet port via an I/O connection, as is the ability to use a Mac mini as an expensive and somewhat awkward IP network router, but it's vastly more common to install an inexpensive gigabit Ethernet network switch, and connect your Mac mini and other equipment to that.

I'd use the switch.

Your router already almost certainly provides firewall and NAT services. Probably also DHCP. Use that router. Or if your router is configured as a "bridge", get an actual firewall, and connect and use that for firewall, NAT, and related services.

I'd not use my Mac as a network firewall. Far too easy to make mistakes on the untrusted network, and accidentally open up a path to exploit. Some app or some package might open that without overt notice, too. And some denizens of the internet are continuously looking for configuration mistakes.

Router/firewall/NAT/gateway box connects to the Ethernet switch, the switch connects to the Mac mini and whatever else is in use on your local network, etc.