1. Cabin: For now while the main story is still presumably in the early stages, a simple wholesome activity like "watch tv" or "play games" to pass a time slot should be enough, alongside of course actions like "talk" where you can add more new sentences and lore with each update. Maybe later in the game different affection levels can produce different dialogue responses to the same questions? This is not that significant but just a little cool addition.
2. Showers: I can't remember if there was a limit or not to the number of times you can visit the showers before a time slot passes. I just remember spamming the showers once I discovered it, and then every now and then spamming again just to check new scenes. I would suggest, to avoid this, that you limit it such that after entering the shower once or twice, time slots move to the next. This encourages players to be less spammy and the showers will be more of something you check in every now and then when doing quests. I think the RNG is good. Since this isn't a one-time event you can't really get locked out of anything (other than the low-affection content like getting finisher'd by Lintar). And new scenes encourage people to use the showers every now and then, alongside the aforementioned limit.
3. Day cycles: Honestly I didn't even notice when playing. Though yes I fully agree it can be a bit tedious if for example an event required being somewhere on a "Thursday afternoon" and when I finally go one full week later thursday afternoon happens to launch another event automatically. Then again, the week cycle benefits you mention definitely are pretty good to have too. So I think as long as you minimise or ideally avoid making "go here on thursday afternoon" type of conditions, the change would be barely noticeable, and with the added benefits.
4. Update type: I agree with @dragonbackmike's comment. Both are useful to have. For chapters with big and exciting story content, say for example if Sabrina's visit to New Kassiopeia evolved into a dramatic fight to escape, then yes I think focused content to finish the 'arc' and develop the relationship with the LI(s) is good. However if its just a 'chill' content update like a quick visit with some lore and relationship developments, it'd be fair to spread out the attention a bit more so anyone seemingly lacking content (or if people want more content on a certain character) has the chance to catch up.
5. Lore dumps: I think its fine as it is, it wasn't too extensive (it gets wordy if you dive into the wiki but dialogue-wise it was alright). I mean, part of the whole experience is world building, that's why we have lore in the first place. What is in the game now is a lot of info, but that's kind of necessary at the start, I imagine its just a slow addition as we go for yet-to-be added lore. Dump the basic info about the world, and add more as the MC learns more (which is what you're already doing). The wiki is already quite well organised, just as long as its kept up to date with the new info I think its fine.
6. UI: I think it could look better, yes. But its not really the biggest issue. I'd say you can make small improvements across a few updates if you don't have the spare time to do it all in one. If I were to criticise the UI specifically, I would say it looks 'simple'. So it's not like unplayable or anything, but definitely could use some surgery.