any alcohol based product should take off the marker... rubbing alcohol, nail polish remover, etc. Work lightly and quickly, as you do not want to remove the finish on the floor.
As for scratches, you can cover them up with....permanent marker. They come in a variety of colors now a days, get the fine point and fill in. At a flooring store, you should be able to find wood markers.
Sometimes you can swell out the scratches. I do it on tables. Put a damp towel (folded up) over the scratch and let it sit for a few minutes. Then come over it with a hot iron. The idea is that the moisture will sink into the crack and the heat will swell the wood back in place. It may swell over the scratch edges. Sometimes I have to hand sand, restain (stain or marker, and put a finish coat over top.
Stephanie