Highlight the white text inside the block for hints ranging from vague to specific...
There are 52 letters (a-z and A-Z) and 52 cards. Most likely each scrap corresponds to one of the 52 puzzles.
Certain clues seem to refer to the contents of certain other puzzles. For example, v appears to be referencing Procrustes puzzle, 10 of Spades.
Exploring mapping all scraps of paper to the previous puzzles.... not sure that this is the right thing to do (yet), but it seems reasonable.
From the story part of the next part, "careful to keep them in order" implies that the order of the scraps is important for extracting the answer.
Unknown at this time.
Speculation and talk about puzzle, contains potential spoilers:
I agree that the 52 scraps must correspond to the 52 puzzles. So far I haven't gotten things to pan out, but I'm not at all confident in my pairings either.
The text states "You can change your fate by adding up what you've found in your journeys through the Maze of Games". I keep coming back to the phrase "what you found". What does this mean? What did "we" find?
If "we" is the reader, then we found answers to the puzzles. If "we" is the children then they, too, found answers to puzzles. They also found a variety of items. Sam, for example, ran through several weapons.
I'm wondering if we are off-track on trying to map the scraps to the puzzles thematically. Given the difficult time we are having there may be a less ambiguous way.
Things to try:
Acrostic on answers or puzzle names
Index into answers or puzzle names by letter value (seems unlikely)
Read down first letter of puzzle names or answers
Proposed Mapping (feel free to add additional potential matches to each scrap)s: