Electrical – Removing a keystone jack from the wall plate

You can buy flat Ethernet cables. I'm betting you could get one under the door and still allow it to be closed.

Another option is a powerline Ethernet adapter. This is a set of modules that plug into your power outlets and allow you to transmit network signals over them. You run a patch cable from the router to a module in the same room, then plug in a second module in the room the second PC is in.

Also, if the rooms are next to each other, look around ducts, pipes that might pass through, etc. You might get lucky and find a gap big enough to fish a cable through.

Another option is to install low voltage boxes in the drywall with RJ45 jacks. Wire the jacks together, color to color, and use patch cables from the router to jack one, and from jack two to the second PC. Just leave them when you move and it will look like any other jack in the wall.

And lastly, have you considered WiFi?

1. I'm no pro, but I'd say you can do as you wish with low voltage cable
2. I'd guess the daisy chaining was a poor mans way of propagating the phone cable without running it back to the closet.
3. Yeah, see the last answer
4. I'd remove the phone jacks and short out two of the pairs with clip leads. Then use a continuity tester to map out the cables.
5. Does the grey one lead to the attic somewhere?

I'd say you can terminate the cables you need with wall plates in the rooms, RJ45 jacks in the closet and if you need additional service to one of the daisy chained rooms, you can add a switch where needed to continue the chain. Mount the switch to the wall close to the wall jacks to get it out of the way.