You have to catch all 5 spirits, so it doesn't count if you got your gems in other ways. Also, in the first update where spirits were introduced, it didn't register them being caught, so if you caught a fire and water elemental back then, you'll have to catch them again.
It depends on the room, sometimes take as few steps as possible, sometimes make no mistakes when solving the puzzle. The more unnecessary things you do, the lower the score.
You have to catch all 5 spirits, so it doesn't count if you got your gems in other ways. Also, in the first update where spirits were introduced, it didn't register them being caught, so if you caught a fire and water elemental back then, you'll have to catch them again.