Do I need a router with Mac and these firewall settings?

Solution 1:

You only need a router if you want to "route" a network connection to more than 1 device.

If you only want to have 1 device connected to your network then you don't need a router. If you add another network-enabled device (TV, printer, another computer, etc), then you will need a router to share & control the network traffic.

Solution 2:

Fsb is correct that you only need a router if you wish to connect to your network with another device.

But this doesn't mean you necessarily have to add a physical router. Instead, you can connect to your modem with Ethernet cable (if you aren't already) and then use the Sharing options in your System Preferences to share your internet via Wifi. This would allow other devices (such as an iPhone) to connect to a new wifi network setup by your Mac because your Mac has become the router for you!