It depends on the system. Most professional CCTV systems only need to be connected to the internet for remote viewing. If you are only wanting to view the cameras on your local network, then they don't need to be connected to the internet.

In the case of this 'Rraycom' system, I have no idea. Until you posted I had never heard of this brand before. Installing CCTV systems in one of the things I do for a living. It looks like dozens of other cheap Chinese systems, that all get stamped out of the same factory.

For your control issues = Rather than use the remote that came with the DVR, you could get a wireless mouse and control it like that. A Logitech M185 wireless mouse is only $15 on Amazon.com. The mouse will give you more control over the interface than the remote control was giving you as well. Just plug the dongle that comes with the mouse into a USB port on the DVR and it should just work.