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What is the K in that last graph (F5) and why did it move compared to previous?

K is the knight or just a knight on a chess board. The numbers represent how many moves to get to each square. Hope this helps

A question I had (which might be the same as the one asked above) was why you chose to place it off-center.

It could be anywhere, the numbers will translate as well. Try to do it by hand as an exercise.