So... is Uchuu no Senshi finished or not?
NO, it is not finished.
Why?
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
Here you have all the anime relations we detected ordered by release date, so you can see the reason for this status in context and also use it as watching order.
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Synopsis
Johnny Rico, a young man from Buenos Aires, is at a crossroads. Unsure of his path, he's spurred into action when his friends, including the object of his affection, Carmen, decide to join the Federal Military.
Driven by a desire to be near Carmen, Johnny enlists as well, hoping to follow her into space.
However, their aspirations take a turn when they find themselves caught in a burgeoning interstellar war against an enigmatic insectoid alien race. Johnny's motivations shift as he's thrust into a conflict he never anticipated.