We use this word in U.S. English but we spell it without the "e." The singular is story, the plural is stories. I live in a two-story house myself. There are two stories. Our bedroom is on the second story. The Empire State Building in New York City is 102 stories tall, and has public observations decks on the 86th and the 102nd stories. A news report says: "The Trump Organization claims that Manhattan's Trump Tower rises 68 stories over Fifth Avenue, although databases such as the Council on Tall Buildings and Urban Habitats say the tower is only technically 58 stories tall."

Yes, you can use it for any number. For 'one' you would say 'single'. I think the same word is used in American English, except they spell it without the E. We certainly use it here, sometimes with both spellings. You can use 'floor' - but that is usually more for taller buildings, rather than houses.