Is Elliott Smith's music public domain because he has died Or who would you have to get the right to use his music in a film?

Answer 1

No its not public domain, and yes you would have to get permission from the copyright holders.

Generally an artists recording contract transfers the copyrights to the record label, for which the record label monetarily compensates the artist. As such, long after the artist has died, the record label still owns the rights to those creations.

Elliott Smith recorded under several different labels during his career, and in order to use his music in a film, you would need permission from whatever label owns the rights to the particular piece you wish to use.