Yes, you can connect a wire to transmit the wireless signal from a wireless router.
Yes, you can connect a wire to transmit the wireless signal from a wireless router.
You can lengthen the antennas temporarily, but this increases signal loss in the cable. For basic consumer setups, it's not a big deal—adding another access point in that room would be much more effective. With two antennas and most MIMO configurations, placing them close together can cause unusual performance issues for your existing AP, slowing down all other users' connections.
Find a way to boost its output so it can manage the load better.
Discover techniques to boost Wi-Fi range with a 2.4GHz antenna using a Wi-Fi repeater.
It should function properly. You can connect the broadband line to the new AP, run two cables for the PC and the wireless router, and position the router in Room B. Alternatively, you could use a different wireless router if needed.