The gacha is something completely unrelated. She wants a Sunday event. The hints of those are on your page. You're probably lacking Hibiki's love points to trigger it. Take the girls to the beach/pool and pick her as much as you can.
Vendena
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The game is made in a way that you won't miss anything, so no worries of doing stuff in a specific order, or stuff like that. There are no timed events, time limits, or similar. That said, the game focuses on intertwined stories, so you can't just focus on a single heroine from start to finish. You'll have to branch to unlock requirements.
You can, though, skip some content. Stuff like Aurora, Platinum, and such are not enforced. The repeatable beach, pool, etc. Ignoring those won't penalty you in any way, other than you just out missing on game content.
Since you're dealing with a mod produced by someone else, I cannot help a lot since I don't know how it works. That said, a bit above the Development Log in this site, you can see where the game stores it's saves. You could try to find where this mod stores it's saves and copy it. This might work or not depending on what the mod does. Good luck.
Ah, the second building bug. You have two options to fix it. Edit your save and change these values:
Location_SB_Bath_Discovered
Location_SB_Door_Discovered
Location_SB_Kitchen_Discovered
Location_SB_Living_Discovered
To True.
Or, wait to July 17 for the game update and ask The Mysterious Heroine VI to fix it for you.
I'm very sorry for the late reply. When you're trapped in her house, to progress all you need to do is talk to either Fumiko or Satsuki at different times of the day. Talk to Fumiko first, if nothing happens, try Satsuki. If nothing happens, return to your room, spend time there, then try again with both girls. Next update will make it easier to figure out what to do, but for the time being, you know you're doing progress because time advances when you interact with either of them.
You need to spend time with Fumiko or Satsuki, during different times of the day.
Talk to Fumiko, if time doesn't advance, talk to Satsuki. If time doesn't advance. Go to your room and skip time there. Then repeat again with both Fumiko and Satsuki.
You know you're doing it correctly if time advances (ex. morning > afternoon).
It's not that complicated. Just spend time with them at different times of the day.
I won't argue on your views of what NTR is or not. You can read about NTR in HERE. This game's approach is more into Polyamory, with one male and several females. I completely understand if you don't like it, though. And respect it. There are hundreds of amazing games in this site, mine not being for you is fine.

