Bit late to this but posting just in case.
Without going too in-depth into the stuff you mentioned;
The bloody torture room in the prison area can be accessed by finding a key in the box puzzle room after you solve it (hint: empty shelves).
As for the injured rabbit, you could give it to the "Shadow Girl, since somewhere at the end of the demo, it hinted about giving more small animals to the girl. Not sure what triggers that dialogue/hint, but the outcome just adds more dialogue to the ending, that is unless there are more than 2 animals that I haven't found.
No clue about the Golden Fish (I'm assuming you mean the one at the Shrine), if the Train Station route is assessable in the Demo (I believe it is another way to skip the forest puzzle), or any purpose during the Dream/Nightmare Sequence with the Red Parts.
There are a few other secrets that I've found; although most of them are either another path to skip a puzzle, something that subtly changes the area, or just leads me to a brick wall (such as the "Fish?").