I swear he's cooler in game than this clip makes him look

you may be thinking of Gothic horror, which definitely fits Delicious in Dungeon. the themes of tragedy and consequences, people going mad with obsession, the past coming back to haunt you both literally and metaphorically, etc.

there's also a genre of 'mafia boss' romances for the same reason, but with a dangerous bad boy angle

replace 'billionaire' with 'prince' and you kind of get the idea. someone important (and wealthy) treating the ordinary protagonist as special is a pretty common fantasy. also works well with the 'I can fix him' motif

It's been a while but I remember having to learn early on that using environmental effects to keep enemy numbers down is a better use for power than power cards. Otherwise yeah it's tough because screwing up one turn can ruin a whole mission.

I think the term you're looking for is "tribalism". It generally applies to anything that has an us vs them, in-group vs out-group mentality.