Let's see:
1) No plans to change the priestess interaction at this point. I am getting close to wrapping things up, so I am trying to focus on either things I wanted to have in the game, things that are unfinished, quality of life changes and the odd, small task which doesn't need too much time to get done.
2) Slut reputation unlocks certain scenes (like the guy in the slums) and it affects the ending you get with the emperor if it's too high (you can't become the empress).
3) I think I could add the Institute to the schedule as an "extra" for either the morning or the afternoon, that makes sense given how it works.
4) While I agree in theory, I am not sure where I could place more fast travel points. Since the schedule was added, fast travel has probably become even less useful. I'll see about adding a "leave the city" option.
5) The task can be completed, but Navarra wants you to be thorough and check all the "candidates" info, even ones where you already found that something doesn't match her prediction (basically, you should have a complete profile for ALL the girls).
Viewing post in Caliross, The Shapeshifter's Legacy comments
1) Totally fair, as I said, that was more of "it'd be neat" than anything I really expected.
2) Is there any way to tell when an action raises it normally? Or is it all really self apparent? Like, you know, you can (sorta) date various characters, does everyone kiss and tell adding to your reputation, or is it only randos/public activity that add to it? etc.
3-4) Reasonable and thanks for considering making any alterations for QoL tweaks this late in design.
5) Oh, fair enough. Yeah, I'll admit I did not find that intuitive. Whether that's something that matters enough to adjust/put in the quest log/w/e, or if it's fine as is is obviously your call.
Actions that are "slutty" and "public" are generally what raise the slut reputation. Working at the brothel or doing some exhibitionist stuff, for example. Being a slut in private or in places where discretion is more expected is fine.
For Navarra's quest, the idea is that her power isn't perfect, so she wants to cross all the Ts. I'll see if I can change the dialogue to make it more obvious.