2. Some pieces can be rotated and flipped.
3. The most interesting rule is that when pieces are the same color, they must be connected at a corner. See 2nd image - reds and greens.
There are 120 free levels and I've done 109. The 'advanced' puzzles are not free, but I haven't gotten to them yet. I honestly didn't think I'd like this game, but I do. I've spent 2-3 hours on this.