People, just put your headcanons here, don't be shy, and if you don't have an account, make one to post here, I'm bored.
Not sure if it counts as a headcanon since I think there's a lot of evidence pointing to it, but I think Kota is almost as big of a pervert as Luke, he's just more discreet about it.
Luke has probably gone to TFF or ACFI to get laid.
When I initially started playing the game I assumed the reason the hotel couldn't produce salt was because salt was once used as currency in ancient Rome. However, it's later stated to be because salt has mystical properties so that headcanon was wrong.
Kota did not put piss in that beer. If he did, it would probably improve the flavor.
Several times we see Kota go around in fundoshi, according to him to be in a more comfortable environment. But considering how he reacted to seeing Luke half-naked for the first time, you'd think he'd be more reserved about such things. That added to how he talks to you and how he behaves when he finds out that you are dating Asterion makes me think that you are right on the first point.
At the start of the drinking game, when Luke asks his test question ("drink if you've ever sucked a dick"), Kota's initial reaction is to look at you and Asterion. It's likely he just wants someone with authority to step in and veto the question, but I think it could also be interpreted as him being curious about your and Asterion's relationship. Though more damning is that depending on which characters are present, he'll get caught cheating (failing to drink) after a particularly raunchy question.
Also, during the scene where he opens up to you, if you play the Speedrunner route you get a unique response option that elicits a very interesting reaction from him.