Okay, these are both in the Underworld (moongate on top of the Demon Temple)
To get into the Puzzle Room, you need to first get the key (1). If it's your first time, make sure to read the book first. Once you have the key, go to the Puzzle Room (2). You must complete the puzzles on the left and right first in order to get the last puzzle. Left and right are both closing a circuit, and the third is like the regular Khaldun puzzles - figure out the sequence.
When completed, you're given an Experimental Gem, which you then take to the Experimental Room (3). I'm not gonna spoil where the entrance is, but just remember, making things disappear will reveal that some things are not at all what they appear
When you get into the Experimental Room, be sure to read the book carefully and memorize the colour/effects, else you'll be screwed right off the bat. You have a timer on the Gem once you start, and if you mess up at any point during the three levels, you'll be expelled back to the beginning to start again. Once completed, you will receive a random reward.
As for the other puzzle, go further in until you reach the Trap Hall, then enter the small room to the East (C), you should see a table with maps and such on it. Doublt click the compass, then go and stand on the first row of pavers. Move along this row until an arrow appears on your compass. Follow the path carefully, stray and you might not survive. Once you get to the Puzzle Box (4), you have to match a picture by finding the right sequence in a set number of moves or less. Once completed you will be given a random reward.