It's not quests actually, just small tasks to get AP. Move cursor on AP status and sometimes you will see that tasks here and time slot limit to complete.
Really? I do not recall receiving that information at all, though I suppose I might have missed it somewhere. There's no quest there at the moment, but I'll try to keep an eye out for tasks showing up.
UPDATE: It took a few days, but a curiosity quest just showed up (about being "penetrated by a guy with a length and fatness of at least 18"), so I can confirm that is where they show up.
UPDATE 2: For posterity, the indicator for an active curiosity quest is a magnifying glass-icon next to your AP.
Another question just became relevant: Since the idea of what would essentially be the current version of romantic interests for a character's male self, namely the bar-girls, explicitly having sex with another man perturbed me, I very quickly and deliberately fed Bruce a Breeder pill, fucked Bree and, according to the dialogue, certainly impregnated her. According to the rules as stated by the game, this should mean that Bruce is now permanently Bree and thus should no longer be an issue.
Yet my character's female self just spoke with one of the bar-girls, only for the conversation to reveal that girl to be fucking Bruce. Is this intended behavior - as in, do I need to get rid of Bruce
again - or a bug?