I've scanned the boards and can't find a similar thread...sorry if this is blatantly obvious.

I've had a website for 18 months now, on a simple package with 1and1.co.uk, paying £5 a month for the hosting package and the domain name. I now want to move away from it, and was recommened KoolMoves by a friend.
Can I keep my domain name with 1and1.co.uk, or do I need to transfer it to another site which works with koolmoves?
Is koolmoves all I need to be able to update/edit my website?
And what about hosting it on the server?

Many thanks.