The first area in Claire.

1st Puzzle : Clock Puzzle (Hospital 1st Area)
Explanation: So you can find an alarm stuck on 3:30 close to the door where you use the doctor keycard. That's the time you set the clock to.
Prize: A butterfly.

2nd Puzzle : Portrait Puzzle (Hospital 2nd Area)
Explanation: You solve this one by flipping over the portraits of those who are alive, leaving only the deceased showing.
Prize: Founder's key. (Item required to proceed in the game).

3rd Puzzle: Power Puzzle (Hospital 3rd Area)
Explanation: You solve this by increasing or decreasing the power in the correct order.
1. Increase power.
2. Decrease power.
3. Increase power x2.
4. Decrease power x2.
5. Increase power.
Prize: You can continue the game.

4th Puzzle : Chess Puzzle (School 1st Area)
Explanation: You solve this one by.. I have no idea. Honestly all I did was spam everything until it worked. All I truely knew was that the broken piece was last. The correct order is: Peon, horse, tower, jester, queen and broken piece.
Prize: A butterfly.

5th Puzzle : Piano Puzzle (School 1st Area)
Explanation: So I tried mashing random keys, I'm assuming the hint is the bear song playing on the TV next to you. There's 3 keys you can press, left is 1, middle is 2 and right is 3. This is the correct order to solve the puzzle: 3, 2, 1, 2, 3, 1.
PS: If it doesn't work, it might be because of the E key. Try switching controls for it in the options and trying again. That or you messed up the order by accident.
Prize: Bolt cutters. (Item required to proceed in the game)

6th Puzzle : House Puzzle (Apartments 1st Floor)
Explanation: So for this puzzle, you have to look at the writings on the walls scattered around the rooms surrounding the doll house. Tammy slips on the wet floor (Bathroom). The dad goes upstairs and shoots himself (2nd floor bed room) and the mother is stabbed by a kitchen knife (Kitchen). That's where you're supposed to set the candles.
Prize: Boxcutter Item used to save someone on the 2nd floor of the apartments

7th Puzzle : Panels Puzzle (Apartments 1st Floor)
Explanation: Those 5 panels (Denial, anger, bargaining, depression, acceptance) all represents the 5 stages of loss and grief. All you have to do is touch them in order, which is the order I gave in the first place.
Prize: Hosting key. (Item required to proceed in the game)

8th Puzzle : Valve Puzzle (Apartments 2nd Floor)
Explanation: Just like the chess puzzle, I went with trial and error. I'm not sure where I could've got a hint for it, thankfully it was easy to do in a way. All you have to do is turn the valves so that little pin faces the right way.
Edit: Adelion brought up a theory that makes a lot of sense, read at your own risk as it is massive spoilers: It could be the time where Claire tried to commit suicide. (3:33 as it's shown frequently in the hospital). The right valve is the clock marker and the left one is the minute one.
Prize: A beating heart, a key item to break the sigil and proceed in the game