Are these tiles only available through the crystal shop? Or is there a chance that I could get them from just playing the game?

It's been some time that I played tiles, but I think you get a tile as reward for the bonus game, depending how much you cleared/played :) I know that I got my tiles from the game.

Yeah, it's better to play the game. It'll take longer, but you can save your crystals for other things.

You have to fill the in-game case and then you play a bonus game and you get the tiles from that