Do you believe In Angels ?

According to the bible and the koran, angels are a very important part of the story of god's interaction with humans. 

Out of curiosity i did a little research and found this list of angels heirarchy in heaven.

    * First Sphere (Old Testament sources)
          o Seraphim
          o Cherubim
          o Thrones (Gr. thronos) (New Testament sources)

    * Second Sphere (New Testament sources)
          o Dominions (Gr. Kyriotetes)
          o Virtues (Gr. Dynamais)
          o Powers (Gr. Exusiai)

    * Third Sphere
          o Principalities (Gr. Archai)
          o Archangels - Archangeloi
          o Angels - Angeloi

Angels of the first sphere work as heavenly guardians of God's throne.

Angels of the Second Sphere work as heavenly governors.

Angels of the third sphere function as heavenly messengers and soldiers.

According to the story the devil was an angel that was sent to earth by god before he created adam and eve. Is this correct?

What puzzles me is when exactly these angels were created in the six days of creation?

If you are a christian or muslim do you believe in the existance of all of these supernatural beings? And what is the difference between the belief in angels and the belief in polytheism?