To get the water from the waterfall, just drag a villager over in front of it. Usually it says "getting a drink" but when the diamond is in the fire it will say "putting water on the firepit". It takes a lot of bowls to cool down the diamond.

I finally got this one. It would never let me get water while the fire was burning. I think the timing was just weird. Had 1 minute left on fire and it wouldn't let me get water to put it out. When the fire went out, then I had the gem.

I have a problem with puzzle 13 for the first time.
My VV3 is running for weeks now and is on difficulty hard.
At the beginning of the game I used to put it on 'slow' at night and when there was fruit on the trees I've put it on 'fast' in order to get the food as quick as possible. I do not timetravel because I know this will mess up the timing of the game and cause malfunction in growing fruit etc.

Adjusting the timing back and forth from slow to fast has caused a timing problem though in the firepit. It says now: 'Time remaining for fire: 225h 40m!!! I've been waiting for the sparkles and the gem to show up but they do not appear!! What can I do?? Anyone else that has this issue?

Changing the game speed can extend the fire timer, although that's usually harmless. It's due to a glitch in how the game handles pausing with the space bar. You can see an explanation of it (and how to correct the fire timer) here.

Thanks Barbara! That helped, my firepit is okay again