Assuming your not forwarding ports to it from the router, just remove its gateway IP address on the server.
This does depend if you want to block inbound or outbound.
Adjust the firewall rules on the server and by default your router shouldn't allow inbound connections. Id just put a block on the router saying block the IP from making outbound connections.
This.
Give the server a static IP.
Thats what a firewall is for.
I'll probably use WSUS, but yes this is a consideration.Do you not need windows updates? (assuming it is windows based)
i would give it a static ip address i wouldld also say its poor practise to have a server on a dynamic ip.
and then i would do as sugested dont put a gateway in.
unless its a dns server then it will need internet access.