If you put a Switch capable of 1000MBit networking on a Hub/Router that can
only handle 10/100 will devices hooked up to the switch assuming they have
the proper network cards work at the higher speeds between each other? Or
is the whole network only as fast as the slowest device, or the main
hub/router?

if all peers in the network have gigE cards and are all connected to
the gigE switch, then all thoes peers will get gigE bandwidth, it's
only the devices hooked up to the hub/router that will get 100mbit
between them and the hub/router. If you enough switch ports then just
use the hub/router as a router (assuming it's to the internet), and you
shouldn't see any downspeed, unless your internet connection is faster
than 100mbit (which I doubt)..

--K-sPecial