After teleporting from the map start you are in a large hall. Run up the western stairway and look to the north to find that one of the sconces is missing a torch. Lower the back wall to find a nukage pool, surrounded by a walkway (sector 66) where some useful items rest on: a plasma gun, a bulk cell, a backpack, a soul sphere and an armor: a green one on hard or a blue one on easy and medium skills.
After entering the red rock cavern east of the large hall mentioned in secret #1, look to the north to see a gray pillar. Drop from the brick walkway beside this pillar and ascend the stairway to its northeast. At the apex (sector 79) you can acquire two boxes of shells, a bulk cell and a megasphere.
Secret exit: Standing in front of the regular map exit, teleport back and pass the door. In this marble room, head to the northwestern corner and look to the southwest to find a section of wall with horizontal lines carved in it. Open it to find a switch that you trigger and return to the brick walkway at the red rock cavern's entrance. Look to the north to find that the gray pillar southwest of official secret #2 has opened to reveal a lava pool; enter it to be taken to another simulation gate. Enter it and you will find yourself in another exit hall with a simulation portal marked "RESTRICTED" and "TOP SECRET". Open the barrier and step into the portal to go to the super secret level, MAP32: Prestidigitation.