Need late game tips, really stuck

I've managed to unlock quite a few things lately but I got to a point where I'm stuck. Checking my notes is leading me nowhere and I find myself kinda wandering aimlessly checking random things to no avail. Please try to spoil as little as possible because sometimes I just need a small push to figure out stuff. These progressively explicit tips from vague to specific are really cool if you have the time.

Stuff I unlocked:

!- All permanent upgrades: Orchard, Outer Room, Satellite Dish, Mines, Blue Tents and Blackbridge Grotto!<

!- Found all additional floorplans!<

!- Solved all 8 sigils and the 8 realms/8 months puzzle!<

!- 7 letters/safes!<

!- Unlocked Ladyship's Diary!<

!- Aced the exam!<

!- Got all blue notes and treasure trove notes!<.

These are the things I'm stuck at:

Problem 1: >!Treasure Trove treasure: I've figured out that using Blessing of the Monk in the outer room spawns the treasure chest, but I can't figure out how to open it. It seems I need a special key that I haven't found yet!< .

Problem 2: >!Tunnel Cabinet Key: I found a cabinet key inside the tunnel after removing the crates, but I can't use in any cabinets in the archives, classroom, basement or lab. Am I missing an existing cabinet or is it still unaccessible!< ?

Problem 3: >!Throne Room: It says I have to reclaim the crown. I've tried to bring both the Paper Crown and the Blue crown to the room to no avail. I can't light the candles, and spawning it in the outer room didn't do anything!< .

Problem 4: >!Blue Door in tunnel: I've removed all the crates and gone through all the doors bug got stuck on the blue door with the big leaf. Am I missing something or am I not supposed to open it yet!< ?

Problem 5: >!Castling: I've noticed multiple tips about how I should do a "castle" with a rook and king. I've tried drafting the office and nook and switching the rook and the king on the chess board, nothing. Tried drafting them next to each other in a corner like in real chess and nothing. One of the tips I saw was "You must don the mantle of the knight to perform the ritual of castling". I have no idea what that means!< .

Problem 6: >!Secret Passage in outer room: It has a new book that is blank and not interactable!< .

I'm aware some of these may be connected. If they are, you can just tip me about the first one I have to figure out.

Thanks in advance, this game is awesome and I hope I still get some amazing epiphanies.