Hi! The rule for increasing the stats is under 10 Hearts rewards. You don't have to roll for it even though it's in a numbered list.
It's vibe based and just depends on what you use. If you use your knowledge its lore (example: I've played this part of the game so I know what to say, I've read about the setting so I know this village has gold, I've read the exclusive comic so I know this love interest's weakness), and basically everything else is love (example: I'm dancing with this character, I'm trying to deescalate by cracking a joke, I'm bandaging this love interest and getting real close).
Roles and backgrounds only matter in the mechanic when it's being used while resolving the dice roll. So it's like you're a healer princess and you use your healing power to heal someone, or you use your princess authority to order someone to bring you herbs, then you roll with 2 d6 and choose the better option. Other than that, it's unrelated and just for narrative purposes.