PART ONE OF TWO:
Did Buck Rogers (1939) create the opening crawl?
This online video: 1
Claims that George Lucas was influenced in many things by the Flash Gordon movie serials of the 1930s, including the opening crawl. And many sources state that George Lucas wanted to make a Flash Gordon movie but couldn't get the rights so made Star Wars (1977) instead.
Episodes of Flash Gordon Conquers the Universe (1940), except for the first one, begin with opening crawls summarizing events in previous episodes.
Episodes of Flash Gordon's Trip to Mars (1938) have a different method of summarizing events in previous episodes. A member of Queen Azura's air force turns a knob on a television like device to show screens with written summaries of past events.
The openings of episodes of Flash Gordon (1936) have static written screens and a voice reading aloud what is written on the screens.
So it appears that the Buck Rogers (1939) serial used such an opening crawl before the Flash Gordon Conquers the Universe (1940) serial did. But that doesn't mean that the Buck Rogers (1939) serial invented that practice. It might have become a common practice in movie serials before Buck Rogers (1939).
I know that that the Buck Rogers (1939) serial did not invent the opening crawl, because the big budget 1936 movie The Plainsman began with an opening crawl, though of course it was not to summarize previous episodes. Instead the opening credits were in the opening crawl. You can watch The Plainsman (1936) online, as well as episodes of the Buck Rogers and Flash Gordon serials.
So the available evidence is that the opening crawl was used for opening credits at least as early as The Plainsman (1936), and was used in a movie serial to summarize previous episodes at least as early as the Buck Rogers (1939) serial. Thus it is uncertain whether Buck Rogers (1939) was the first movie serial to use an opening crawl to summarize previous episodes.
Bruce Calvert's answer to this question: https://movies.stackexchange.com/questions/104343/origin-of-movie-opening-crawl2
has a link to a fascinating and informative article about the origins of the Star Wars opening crawl, which apparently is rather complicated and somewhat mysterious.
PART TWO OF TWO:
Was Buck Rogers the main and/or only source of the science fiction elements in Star Wars (1977) and its sequels?
I doubt that any elements of Star Wars come uniquely from Buck Rogers, Flash Gordon, or any other single source. I think that George Lucas & co. were aware of all the plot elements and science fiction concepts in Star Wars from multiple non science fiction and science fiction movies, movie serials, television shows, radio shows, comic books, comic strips, novels, short stories, etc., etc., that they were exposed to during the decades it took them to become old enough to work on Star Wars (1977) and its sequels.
I am somewhat younger than George Lucas. I became a fan of written science fiction when I was twelve, and before that I was exposed to a number of science fiction short stories, novels, movies, television episodes, comic books, and comic strips, for children and for general audiences, and so was already aware of a number of science fiction concepts.
Written science fiction stories became increasingly popular in the late 19th century and early 20th century until in 1926 Hugo Gernsback created Amazing Stories the first magazine entirely devoted to the new science fiction genre. A few other science fiction magazines were created in the 1920s and 1930s. And these were the inspiration for science fiction comic strips that popularized science fiction concepts.
For example, Philip F. Nolan's Armageddon 2419 AD in Amazing Stories, August 1928, introduced the character of Anthony "Buck" Rodgers, who became the star of the Buck Rogers newspaper comic strip in 1929. The Flash Gordon comic strip was created to compete with Buck Rogers in 1934, and it is said that:
One source for Flash Gordon was the Philip Wylie novel When Worlds Collide (1933). The themes of an approaching planet threatening the Earth, and an athletic hero, his girlfriend, and a scientist traveling to the new planet by rocket, were adapted by Raymond for the initial storyline. Raymond's first samples were dismissed for not containing enough action sequences. Raymond reworked the story and sent it back to the syndicate, who accepted it. Raymond was partnered with ghostwriter Don Moore, an experienced editor and writer. Raymond's first Flash Gordon story appeared in January 1934, alongside Jungle Jim. The Flash Gordon strip was well received by newspaper readers, becoming one of the most popular American comic strips of the 1930s.2
Since the Buck Rogers comic strip was older than the Flash Gordon comic strip, science fiction came to be described as "that crazy Buck Rogers stuff" instead of "that crazy Flash Gordon stuff". But if one tries to trace science fiction concepts to its first publications most will originate in written science fiction years before the Flash Gordon or Buck Rogers comic strips began.
So the Buck Rogers and Flash Gordon movie serials, based on the comic strips, were obviously heavily influenced by those comic strips, which in turn were heavily influenced by written science fiction stories. The science fiction concepts of the Buck Rogers and Flash Gordon movie serials are based on those of the written science fiction stories of the 1930s, 1920s, and earlier.
In fact, most of the science fiction movies and television shows made in this millennium do not have many - and in some cases have absolutely no - science fiction concepts that were not already published in written science fiction stories by the time that Flash Gordon Conquers the Universe (1940) was in theaters and the golden age of written science fiction had begun.