Will I owe royalties to artists associated with the following music
and films if they are played at a public gathering:
Vangelis
Mozart
Doctor Zchivago (film and soundtrack)
Passion (soundtrack)
Chant (CD title)
Golden Brown (song)
Hernando's Hideaway (song)
Dmetri Shastokivich
Troy (soundtrack)

Yes.  Even as to those old compositions by Mozart that are in the
public domain, the artist who performed and recorded them has rights
in that new performance/recording.  Plus, all the other works are
likely far too new to be in the public domain.

Have you contacted ASCAP about a blanket performance license for these works?

?  Every time someone sticks a CD on for a community center dance or a
town's  holiday park exhibit or an arts-and-wine festival, they owe a
royalty??  Seems unlikely to me.  When you purchase and pay for a
musical recording, the right to play it comes with the package.  What
does a researcher say?

Archae0pteryx

archae0pteryx,

Indead the right to play does come with the purtchase. However, it is
limited to privte, non-commerital insinstances.