Let's stick to the steps I've outlined, login to the camera and change the settings.
So I can't login the camera (unless I try a ssh...?) and update fw nor update network settings.
Sure you can. Grab the Ethernet cable that goes to the camera and plug the other end directly to your PC/laptop.
On the PC go to your TCP/IP settings and manually update your IP to 192.168.0.2/255.255.255.0.
Open web browser, login to the camera and update the TCP/IP settings. Preferably set it to DHCP. As soon as you hit save/apply you'll loose contact with the camera, that's OK. Unplug the camera, connect it to the router.
Change back your PC TCP/IP settings to what it was and continue with your testing.
If you don't get it working, post your entire config from the router.