Thanks for the extended report. I reformatted each of your points down below.
1) Quest Book + Inventory:
So this is a bit tricky since I had to rewrite portions of the school map code. However one work-around to get the inventory and quest book icon to reappear in your old saves is to click on a location and then rollback (mouse wheel up). Or go to Courtyard --> Back to school map.
2) Scene Gallery
For the scene gallery or "Kana's Memories", it's current intended purpose is primarily as a replay gallery for spanking scenes only. The decision to remove the dialogue during certain scenes was a common feature request submitted by supporters in an old "Feedback Survey" I had for (v0.3.1.1), a feature that I agreed with and implemented.
A full scene gallery, one where each (Day + Location) is cataloged would be a large undertaking. So while this isn't something that I would add in the near future. It might be something I can add in the final release/update of the game if the demand for such a feature justifies the development time needed. But I do agree that such a feature would be nice and convenient to have.
3) FPS Drop
Regarding the FPS drops in animations, does this only occur in replay mode? In other words, the FPS drop only occurs during replay mode but not during normal story mode game-play? If this is the case I will take a look since this does sound a bug and I have a hunch on what the issue might be so I'll add this to my list to address in the next version. Your gpu should definitely be able to play them just fine, so I appreciate that you provided this information.