1) Yes it should work although a USB connection will place an overhead on the cpu, connecting via a lan cable would be better.
2) Yes, you should make sure your laptop has a wireless card, built in is preferable but a pcmcia or USB one will do if you see a laptop you like without built in wireless. Any router you buy for a BT should be ADSL, the setup should be performed with a direct cable connection and not the wireless card, the vast majority of ADSL routers come with the required cable to do this. Your laptop should come with an ethernet port to enabe direct connection to the router for initial setup (check specs just in case). The ADSL router will, as you suggest, plug straight into the your telephone socket via a filter (again, supplied with most ADSL routers).