Can I use a fat free milk to make the sauce? Should I add more butter to the roux if I do so?
Yes. The important fat is the one the starch first goes into. The higher temperature reached by fats (as compared to water or milk) helps cook the flour, creating flavors. The liquid added later dilutes the mixture into a sauce. The liquid's fats are not as crucial for the sauce's thickness as the liquid's proteins.
I think of the cooked butter-flour mixture as a thickner that can be added to milk, broths, and even a saucy dish. The roux thickens way better than just a slurry of flour and a cold liquid.