This has the potential for some tricky puzzles! The last one threw me for a bit before I realized that:
a) The first three instructions cancel each other out--mirroring over y, then rotating 180 degrees, and then mirroring over x produces no net change in the image. This was a nice "aha!" moment when I was solving it. You could use facts like these to make puzzles that look more complicated then they really are.
b) You can solve any puzzle by first placing the tiles such that they form the completed image in the frame and then applying each operation to the tiles in order. So if the first step is to mirror the pieces horizontally, you swap the tiles with their horizontal neighbors. Then, if the next move is a 90 degree clockwise rotation, you move each piece one space clockwise around the board. Following this strategy, the completed image will form the full loop, though it may be rotated.
Also, I noticed that the mirror operations in the last level seem to be flipped. So the horizontal mirror operation was flipping the pieces vertically instead. Still, I enjoyed the game!