Clean plexiglass acrylic parts with warm water and mild liquid detergent, wipe with a soft clean micro fiber cloth (or similar). Novus or Brillianize plastic cleaner and polish works extremely well too and they sell the proper cleaning cloths which I recommend also. Do not use abrasives, paper towels or Windex. I would sell Novus and Brillianize here, but it's easy to find on Amazon or elsewhere online.
Hanging Your Atomic Mobiles
A simple j-hook in the ceiling for each mobile or column works best. A traverse rod works well too, such as IKEA VIDGA or similar. You can also hang from L brackets attached to the wall.