A home with no stairs can be as luxurious as one with many floors. It depends on the design and the materials used to construct and finish the home.

You can use natural stone like marble for floor but do not use granite for floor at all as it is very slippery when wet. As for tiles do not go for glazed vitrified tiles for the floor for the same reason. ( floor becomes slippery once wet and may cause mishap) Go for ceramic anti skid tiles that are specially meant for bathroom floor. For wall tiles you can use whatever you like and then decide over the matching anti skid floor tile/ marble. Double charged vitrified tiles are usually used for flooring in rest of the house.

16"ft (wide) front and 31"ft back (long)

A tricky question! Wall to wall carpeting is not a good option in India due to our hot climate as they tend to radiate heat and makes the rooms hotter. That said, they do add an aesthetic appeal and a decor feature when used in the living area. The choice rests with the individual.