No. The two were never in any film together.
Although off-screen the two were good friends, I don't remember them in a film together.
No. According to IMDB Jeanne Cooper didn't begin her movie career until 1953 when she played "Myra" in "The Redhead From Wyoming".
Yes
John Wayne's first movie appearance was not in a western. He is first seen in the movie "Brown of Harvard" in 1926; in which he plays a football player and has no speaking part. His first Western role was in "The Big Trail" (1930) but his breakout role was nine years later in John Ford's "Stagecoach" (1939), the movie which made him a box-office star. When the TV series "Gunsmoke" premiered on TV in 1955, Wayne introduced James Arness in the starring role. (see related link)
If you mean the John Wayne movie then 1939
Stagecoach (1939)
Rhett Butler
No, he does not. By 1939, Wayne had starred in dozens of films and was a well-known face in Hollywood, even if most of his films were made in Poverty Row. There is no way he could have appeared in this film without it being noticed.
Jeanne Granier died in 1939.
Martha Wayne was created in 1939.
Thomas Wayne was created in 1939.
Wayne Handley was born in 1939.
Wayne Proudfoot was born in 1939.
Jeanne Bice was born on July 20, 1939, in Fond du Lac, Wisconsin, USA.
William Cooper - cricketer - died in 1939.
Jeanne Lee was born on January 29, 1939, in New York City, New York, USA.
Doyle Cooper was born on July 2, 1939, in USA.
Patrick Wayne was born on July 15, 1939.
Wayne Henderson - musician - was born in 1939.
J. Wayne Littles was born in 1939.