Me again :)
it should be a fairly seamless changeover, one goes off new one comes on pretty much straight away.
it would appear that BT had a few problems last night, check here to see if that includes your area before I go plunging to much in depth on this one :)
http://www.btbroadbandoffice.com/business/help /ss/0,,Broadband_0_5_BTCTB_Home,00.html
Yes the lights on the router will look pretty much as normal even if it's not connected (I know daft innit!!)
you can possibly use your BT router to connect to your sky broadband, but there is a username and password stored in the router which would need to be changed to the sky ones, I only say possibly as BT sometime lock their routers so they will only accept bt usernames.