That's a new one on me. Military sci fi is its own sub-genre.
Yes, but genres should be described by inclusion, not exclusion. Just as you can have a "space Western", which has the tropes of both sci-fi, and westerns, you can be Space Opera and Military sci-fi.
Star Wars is iconic space opera - lots of war there, it is in the title, even. Babylon 5 is space opera - the main characters are mostly career military, and there's several wars in the 5 years of the series. Battlestar Galactica is space opera.
Starship Troopers (either book or movie) is Military Sci-fi, but most wouldn't call it Space Opera.
"Space Western" could cover everything from Star Trek TOS to the Mandalorian, but I don't think its generally considered a formal genre
There is no such thing as "formal genre". But, as evidence, the following is a comic book cover from 1952: