Having the lowercase I in Imperial Stormtrooper just looks weird, even though it is technically correct. The question really boils down to what medium you're in. If you're writing an article or series of articles on the clinical subject of Empires and their troops, then yeah you'd probably decapitalize imperial when refering to soldiers in their armies.
But since this is a form of entertainment, and weird things like that pop someone's willing suspension of disbelief once in a while, it's probably better not to distract your reader for technical perfection's sake.
Also, yeah the Opera Scene measures the timing of words being on the screen pretty weirdly, I never have known exactly why, probably something to do with the switch for a 'text clear' being timed to a certain beat of the music with Delay Tags (in FF3usME they look like <Dx> where x is a numerical value of how many time periods to wait. it's something like .25 seconds = 1).
You can't quite fit every single word of the Opera in and just plug it in and expect it to refresh the boxes on tempo correctly, it takes a bit of finagling. Being the music head I am, I couldn't resist such interesting work.
I haven't played this game yet so forgive me if I'm wrong, but unless "Imperial" is a proper noun in the game, the "i" should be lower case.
This condition is technically met, to be honest. They're referred to as the capital e "Empire" for most of the game, with only a "Gestahlian Empire" here or there if I recall correctly.