Does varnishing floors create a fire hazard?
Depends a lot on the specifics of the finish, but the most common finish, water-based polyurethane, does not create a fire hazard. Neither do other finishes, but some of them are mixed with solvents that make them easier to apply, which can be highly flammable. These solvents evaporate out, and won't be a fire hazard for long, but will be while applying. So when applying such finishes, you need to be careful with heat sources in the area, and especially make sure you dispose of the rags you use to wipe off things like shellac or tung oil quickly and safely.