IIRC, Lucas was trying to differentiate Star Wars from hard science fiction, like 2001. Magazines like Cinefantastique took issue with the term, possibly because they felt the movie was a step backwards from THX-1138.
Flash Gordon is definitely space opera, and we all know Lucas originally wanted to make an FG movie, but couldn’t get the rights.
Yes, while Flash Gordon predates the term, it definitely is. In fact, according to Wikipedia, Star Wars is considered a space opera. It came as part of a movement in the 70’s that asserted that space opera was not just the old stuff, but was still being produced. https://en.wikipedia.org/wiki/Space_opera
And being in the writing and publishing business, one of the things I have spent a lot of time on is what is a genre and how to define it. Part of that is sticking to what is in use and not inventing your own. Book sellers don’t want new genres, there are enough already. Unless that new genre comes with something very popular and can sell books. Science Fiction and Fantasy are pretty stuck. Even the Vampire craze has been confined to the urban fantasy genre title.
Currently Amazon has no genre called Space Fantasy. Star Wars is listed under Space Opera, which is under science fiction.