You could put just the router in the hall and either connect wirelessly or run an ethernet cable from the router to the computer.
Continually turning off the router will slow it down. Every time you turn the router on it spends some time (anything up to a few days) optimising your connection. Every time you turn it off, it forgets all that and has to start over. The whole point of a router is to provide an "always on" connection.



