Pieces that end up somewhere new: 76 of the 130 mirrors. 54 other pieces stay where they start.
Hint 2
Start: swap the Wizard with the 17th top mirror from the left, swap the Wizard with the 15th top mirror from the left and swap the Wizard with the 16th top mirror from the left.
Hint 3
Finish: swap the Wizard with the 2nd top-left mirror from the left, swap the Wizard with the 1st bottom mirror from the left and swap the Wizard with the 6th bottom-left mirror from the left, then head for the exit.
Pieces that end up somewhere new: all 7 crystals. 1 other piece stays where it starts.
Hint 2
Start: push the 4th middle crystal from the left right 2 tiles, push the 5th middle crystal from the left right 3 tiles and push the 5th middle crystal from the left up.
Hint 3
Finish: push the bottom crystal up 2 tiles, push the bottom crystal right 4 tiles and push the bottom crystal up 2 tiles, then head for the exit.