充數 is right, wireless router won't work for your case

In your case, you basically already have a wireless network. So all you need is to have a wireless adapter for your computer. If you have strong enough signal in your room, a USB adapter is most convenient. Check electronics or computer stores like bestbuy, compusa and you will find the right one for you.

Yes, check with your landlord how many computers are allowed to connect to the network simultaneously