The polishing powder I am using is leaving a film on the surface of the marble. This film has a rainbow color appearance. What is this and how can I prevent it?

Certain brands of polishing powders contain shellac. If the powder has a yellow to gold tint to it, then it may contain shellac. The rainbow appearance and film is the shellac. Chances are you are using too much powder. Try repolishing the marble with less powder or try using a different powder.
Also make sure that the marble has not been waxed. If there are any wax residues on the floor, they can also cause this rainbow discoloration.
TIP Try using a pure white marble polishing powder. Stay away from the colored powders if you are experiencing this rainbow film.