1) If the phone socket has been physically disconnected, it'll need BT to re-connect it (charge of �120 or something). Else, it should be easy to get them to reconnect on a new contract with them.
2) You plug a microfilter into every single phone socket that you use -- whether for a phone, or router, or both. The filter splits the phone line into a socket for a phone, and a socket for the router. No other splitter required.
3) Router is plugged into microfilter, into phone socket. Then either a cable or wireless to the PC (this is up to you, but it's good to set up for the first time using cable).
4) Make sure you go for a wireless router+modem box. (Some are just routers, not modems, but you'll need a modem too.)