Yes, they do have the right to charge you! they are not obliged to send you the disk!
I would imagen that it would be ok to install XP home on the PC, as you do have a valid CD-Key on the laptop I donot se a problem with doing that, as you have paid for the serial.
as for the warenty, I belive that the warenty only apllies to hardware, and since the laptop is running XP Home anyway, you are effectivly doing nothing more than using the revovery console.
The only thing is, I would possible refraing from deleting the "Recover Drive" partition during windows setup as this MAY void the warenty (but I am unsure)
Oh Gay my sig got removed!