No they are pulled from a chess puzzle database. But it sounds like an interesting approach to generate them. Can't even think of an algorithm which can handle this.
If you don't clear the world you'll get new puzzles and start all over.
To be honest I'm not sure if this is the best approach. I think about changing it to getting. New puzzles when you press a new game button.
They are differentiated by difficulty, aka the number of mates you need to win. It's a simple CSV file where I have listed each level with it's mate count. If I later on want to add a harder difficulty, I can easily add another column with a higher difficulty.
They don't have different themes, I just look for mates. The reason for that is I myself only understand mate puzzles. The other types just let you do x moves and you have to end in the best possible position. That's something for people who can play chess on a decent level.
