The puzzles:
Puzzle 1: Fire
Requirements: (none).
Take an adult villager to south-west of the village, and drop the adult villager on the wood, next to the broken hut. Where he/she will take some wood to grey stones, in the village centre. Then, take an adult villager to the north-west of the village, and drop the adult villager in the corner, until the villagers action line says "Gathering dry grass". After the dry grass has been taken to the rocks, where the grey stones are, and the pile of wood, take an adult villager to kindle the rocks and wood.

Puzzle 2: The Dam
Requirements: You need level 2 of engineering.
Grab an adult villager and drop him/her on the rocks, just near the bottom of the pond. Where he/she will say "Building a dam". This takes a lot of time, so you might as well spend that time up on finding mushrooms and collectibles if you still have kids.

Puzzle 3: The scarecrow
Requirements: Completion of puzzle 2.
Take an adept or master farmer to the twisted vines and wood, which is north of the research table. You'll have to do this two times to get the full scarecrow. You'll need to do this, or birds will eat you're crops!

Puzzle 4: Cutting Tools
Requirements: A master Scientist and level 2 exploration technology.
Take a master scientist to the wood and vines, north of the research table. He will "see something", drop him on it. Then after the master scientist has taken the item back to the research hut, drag him back into the same area, this time, take him to the roots, so the line underneath his action line will say "You need a special type of wood to make the tools." Now, the roots are the wood, so let the master scientist take the wood back to the research hut. And you've completed this puzzle!

Puzzle 5: Herb Mastery
Requirements: (None).
Take an adult villager to 6 herbs, each time they've successfully studied it, it will say something like you're villagers have mastered this plant, and you can move onto the next plant. Here are the locations, in a a clockwise direction from the ocean:
In the north-west corner, where the ocean and the sand meets, Herb 1: Drop a villager to the purple flower, that's leaning just over the rocks.
Herb 2: Drag an adult villager to the blue rose, just between the thorns that are blocking the cave, and the silver rocks. Now, drop the villager on that herb.
Herb 3: Look for a tiny blue flowers, that are kind of bundled together, next to the silver rocks. Then drop the villager on the herb.
Herb 4: This herb is like the last 2, it's around the graveyard. Look for a string of purplish black flowers. And drop the villager on the herb.
Herb 5: Look on the south side of the vines that look like there covering the wall, next to the pond. And look for a pinkish red flower, drop the villager on it.
herb 6: Look around the bottom of the island, for an orange flower, and as always, drop a villager on it.

Puzzle 6: The Elder Totem
Requirements: (None).
You need to make a villager master 3 skills, this villager will be known as an elder. You should get a totem after this has been achieved.

Puzzle 7: Sustainable Fishing
Requirements: Level 3 farming, and a master scientist or a master farmer.
After fishing for a long time, algae will grow in your ocean and your fishermen will refuse to fish and will say that they are disgusted by the algae. So grab a master scientist or a master farmer, and drop them in the pond. And the villager says that he/she identifies algae-eating fish. This fish looks like the Canary-Fire-Arrow from Fish Tycoon, and let the villager take the fish to the ocean, let her/him do this about 10 times.

Puzzle 8: The Vine Wall
Requirements: Level 3 culture, and completion of puzzle 4.
Drop a villager to the wall on the east that is covered with vines. And he/she will go and get the cutting tools, to cut down the vines. This may be a while, but not too long. And when you do complete it, you can drop a villager on the wall to reveal a message. Here is a screenshot of the message:


Puzzle 9: The Stew
Requirements: level 2 exploration, completion of puzzle 1, at least 1 of the flowers mastered, and retrieved the cauldron, from the pile of wood.
To make stews follow this method:
1. Take an adult villager to the cauldron (after you find it) where that villager's action line will say "Preparing a stew".
2. Take the villager to the cauldron again, so he/she will say "Adding food to the stew" and do this again, until he/she says "Adding water to the stew".
3. Now take the villager to the herbs, that are around the island, until 3 herbs have been put into the stew.
4. Let your villages enjoy the stew! If it's a good one!

Puzzle 10: The Ancient Mosaic
Requirements: Level 3 of culture and engineering and completion of puzzle 2.
Drag a villager to the ancient ruins, and let the villager "uncover the ancient ruins." This puzzle takes quite a bit of time.

Puzzle 11: The Hospital
Requirements: Level 3 engineering and medicine.
After gaining level 3 in medicine and engineering, you should see a starting of a 2-digit hut, near the bottom of the island. Take an adult villager to it, so he/she will say "Building a hospital". And wait for them to complete it.

Puzzle 12: The Sewing Hut
Requirements: Level 2 culture.
After gaining level 2 culture, you will see a new hut, that is right at the bottom of the village. You have to get your villagers to build it. When they have, you can drag a villager to the hut, and buy new cloths, but it costs 5000 tech points to change.

Puzzle 13: The Sunken Gong Piece
Requirements: Completion of puzzle 9, and a certain stew.
After making the right stew, which is 2 of the red flowers, and 1 of the black flower. Make a villager eat this stew, and the line below the villagers action line will say, "Strange stew... your villager feels the the need to not breathe!" Then take this villager to the 'slide' part of the pond, then wait for a few seconds, and the villager will pop up again, and will take the sunken piece of gong to the research hut. And you've completed this puzzle! Or you can complete puzzle 8, and look at the writing and stuff on the wall.

Puzzle 14: The Inlaid Gong Piece
Requirements: Completion of puzzle 10, and completion 6.
Drop an elder totem on the middle of the mosaic, to reveal a piece of gong, pretty easy really.

Puzzle 15: The Boxed Gong Piece
Requirements: 3 master builders.
Drag the 3 master builders to the crate on the beach, where they will use there strength to open the expertly sealed crate.

Puzzle 16: The Overgrown Gong Piece
Requirements: Completion of puzzle 4.
Take an adult villager to the thorns, where he/she will get the cutting tools to cut down the thorns.