are there any muslims who don´t believe in everything that the Koran says?

I mean, most catholics that I know would disgregard the bible as pure fiction, fantasy, an alegory. Surely I don´t believe most of the teachins and stories in the Bible, but I like the overall message of God´s existence, and peace.

or maybe am just a terrible catholic girl.

Are muslims allowed to question the Quran?