They are the same person, his real name was James Douglas Morrison, However, he went by Jim.
yes
He isn't really called John Morrison, so no. His real name is John Hennigan.
No.
No
no. They did play together once in L.A. though.
Jim Morrison - Profile
Jim Morrison Talks About 2011 Jeep Lineup
Top 10 Musicians Who Died Before the Age of 30
Ray Manzarek Remembers The Doors at the Whisky a Go Go