Consider a Single "guess row":
It can have 5 Wrong entries - 1 Possibility
It can have 4 Wrong entries - (5/1) x 2 Possibilities (the remaining 1 is either Correct or Partially Correct)
It can have 3 wrong entries - (5x4/2x1) x 2x2 Possibilities (the remaining 2 are either Correct or Partially Correct)
It can have 2 wrong entries - (5x4x3/3x2x1) x ...
[EDITED to add:] No, this is wrong at present. For instance, my analysis assumes that you can have a row looking like GGGGY, which of course isn't possible because there's no other place for that last letter to go. That might possibly be the only way in which it goes wrong; I will think about that later, if someone else hasn't posted a more correct answer by ...
First of all, let's put this into mathematical language:
We're looking at the action of the group $S_5$ on a set $X$ of 5 elements $A,B,C,D,E$. Specifically, we're interested in the subgroup $H\leq S_5$ generated by three 3-cycles $(A,B,D)$, $(A,C,D)$, $(B,D,E)$. I will prove exactly what subgroup $H$ is, and thereby answer the two questions you gave.
From the description of the puzzle, the underlying physics is the optical effect called moiré.
I surmise the transparent sheet has parallel strips of altered refractive index, with the same spacing as the dark lines on the cards or very nearly so. Moiré patterns appear wherever the printed lines are not perfectly straight.
See WP for an explanation, and ...
I noticed the arrow sets looked like
And converted them into letters which appear in the corresponding words:
Their scrabble indices match the sum in the red rectangle:
Anagramming the letters give the final answer:
The first puzzles
The third blanket
This suggest the following rule:
The last blanket
The last puzzle
The puzzle is completed!
So now we know the final solution!
Some more notes on the final answer