The USB 2.0 device should work with USB 1.1 (at slower speeds) if it is marked as being backwards compatible, as far as I know. Some devices can be picky and usually state specifically on the back that they will not work with USB1.1 (usually high bandwidth devices like video capture units and the like).
Normally you can't convert USB1.1 ports to USB 2.0, but you can buy a PCI card with USB2.0 compatibility relatively cheaply. Such cards may come with a firewire socket as well.