I only played through the demos twice, so my memories are still hazy, so correct me where I am wrong!
Edmund's Quest
One of the guard towards the southern area of the prison will drop two keys when slain. Now go to the cell in the middle of the prison and you will be attacked by a ghost. Use crushing weapon against it (there's one club lying near the beginning of the game. Use ALT to see it. One guard shall drop it). Don't use magic agaisnt it.
After killing (killing...?) the ghost, read the note and go to the lower left-hand cornere cell. There's a blanket there. Click on it to reveal a tunnel leading down. Note: reading Edmund's note is optional. The ghost is just there for the much needed experience points.
Talking skull
After climbing up the rope, there's a room filled with meats. On a table is a talking skull. Click on it for a quest. After completing the quest, return and speak to the skull again for a reward.
Shrine of the Damned One
Click on the protrait within Fergus' room. This will open a hidden door to the south which lead one mana shrine, one health shrine and a wine casket. Inside lies a permanent survival potion.
Lever Puzzle
The solution is in the note on the writing desk. After releasing the door, pull the lever close by the entrance to disable a trap.
Thirsty Prisoner
Get 2 bottles of water from the kitchen (where the Impish cook is) for the prisoner to unlock Survivor -> Trap Detection skill-path.