What is a general expression for floor, carpet and tile?
A floor means, essentially, bottom part of whatever you're talking about, the part you would walk on if you were walking on it. You can have an ocean floor or a forest floor, for instance. These days, a floor usually means the one in a building, but it used to mean and still can mean the ground or the sidewalk if you're outdoors. Flooring(or flooring material) means something much more specific, the stuff that's on the floor of your house which is primarily intended to look nice. Underneath that stuff is the real floor of the house, usually called a subfloor, which is part of what keeps the house standing, part of the structure. If you wanted to know if someone has tile or carpet in their house, asking what kind of flooring they have would be the clearest way of asking that. Asking what kind of floor they have says the same thing but isn't quite as specific.
I would say What type of floor covering do you have? Even if the answer is wood, tile or linoleum people are likely to answer with the information you need. The answers would be on the lines of ..Oh, we have a wooden floor...., or We have carpet... etc.