Is there a Santa Claus and who is it?
While there was a Saint Nicholas who existed in history the current "Santa Claus" is a fictional character used as part of the celebration of Christmas.  

According to the narrative Santa Claus keeps a list of boys/girls and tracks to see who has been good and bad.  Based on this list he will fly around the world in a red sleigh pulled by reindeer.  As far as entering each home he will use a chimney if available or some other means.

The historical Saint Nicholas of Myra who was born around 270 A.D. has attributed to him the habit of secret gift giving to those in great need and not expecting it.  

Current western culture representations of "Santa Claus" have their roots in an ad campaign commissioned by Coca-Cola with art by Haddon Sundblom and debuting in the 1931 editions of the Saturday Evening Post and other magazines.