This is a true story which happened in Reykjavik, Iceland. The real name of Baddi is Bóbó. He was known as "Bóbó á Holtinu".
The Elvis tribute band was initially not supposed to be in the movie at all, but when attempting to get clearances to use the original recordings proved far more expensive than anyone had expected, a group of professional, Icelandic session musicians were hastily hired to provide the incidental numbers. So the "band" that features in the film is not comprised of actors but of real musicians, really performing.