I think a KVM switch is what you’re looking for. I’ve never used one but from I understand they do is pretty close to what you’re looking for. I used to run some software ages ago that would let me use a keyboard and mouse on a second computer as if it was another monitor but I can’t remember the name.

As for controlling the BIOS I’m not sure if you’ll find a 3rd party solution. Dell servers for example come with a special device called an iDRAC which does do what you want over the network but it’s obviously for Dell servers only.

Should be fine. A switch will only route traffic to the ports where it needs to go. It builds a table so it knows what devices are on what ports.

That router specifically is what made me go small office route with my network and have a dedicated router, switch, and wireless access point. I got tired of diagnosing weird Internet problems but after setting up my network I pretty much eliminated any need to troubleshoot my network since it’s been rick solid ever since. Some knowledge of setting up networking was nice to have so I could do that.