Is a VPN connection required? Or can I do this without VPN?
Either VPN or a public IP will be required. From one of your screenshots it looks like you have an IP. The next step towards making make the printer reachable from outside is to setup Port Forwarding. It can be done from the Network → Firewall → Port Forwarding page. The idea is to set up a rule that forwards all incoming outside connections aimed at the printer to the printer's private IP/Port. For example:
The WLAN printer does not yet get an IP from the RUT955. What is missing?
The page looks frozen, so it could be bugged. Can you try Ctrl+F5? Also, which FW version are you using? (Seems the page is well on the latest version.)
Also, this page shouldn't have an effect on the actual results. In your Wireless information screenshot it looks like a device is already connected via WiFi, could be the printer. You can check its IP in the ARP table, which can be seen in the Status → Routes page.
I would also like to recommend configuring a static IP lease for the printer so that its IP address always remains the same. More info on that here.