"Does furniture movement damage the surface? "

Only if you drag your furniture across the floor - in which case pretty much any laminate, wood or bamboo floor would be damaged as well.

Cork maintenance is similar to hardwood. It should be cleaned the same way. With heavy furniture, you will see dents in the floor when furniture sits for a long time, however, cork has a certain amount of resilience, so eventually, the dents will fill in and disappear. I recommend sealing a cork floor (even pre-sealed) with a polyurethane, as it is prone to fading from direct sunlight.

What is the mfgr. and pattern name of cork floor?