No, The Last Exorcism has nothing to do with The Exorcist or its sequels and prequels.
No, The Exorcist, film and book are based on an exorcism that the book's writer, William Blatty had heard of while he was a college student.
Exorcist
1973
"The Exorcist" is a work of fiction based on a 1971 novel by William Peter Blatty. While the author claims to have been inspired by a 1949 case of exorcism in Maryland, the events depicted in both the book and the film are fictionalized for dramatic effect.
"The Exorcist" (1973).
The film version of the Exorcist?
The Exorcist
Patrick Swayze last film was the lead in an ill-fated A&E TV Series
As of May 2015, there is no evidence there will be a remake of The Exorcist. However, there is a television show that debuted on September 23rd 2016 on FOX based on the movie series. It remains to be seen if it will be successful.
His last project was the television mini-series "Ellis Island" (1984). His last film was "Nineteen Eighty-Four" (1984).
Movies like "The Last Exorcism" like to state the line "based on a true story" - which means the storyline was borrowed from an actual happening, and the movie may have some kernel of truth in it. But most of the time the story in the movie is highly exaggerated.
The Exorcism of Emily was directed by Scott Derrickson. He also directed movies such as Goliath, The Day The Earth Stood Still and Hellraiser: Inferno.