Sometimes what Quran tells us contradicts with some of the Muslim beliefs, mostly because of the hadiths. For example:
The great flood is not mentioned in Quran as a planetwise disaster, rather it could easily be interpreted as a local disaster, which only wiped out only one tribe/nation. There are many other examples of nationwide natural disasters in the Quran, espacially the description of one is highly looks like a volcano explosion.
The splitting of the Moon is an event that not yet happened according to Quran. It will happen in the last days of earth, while the humankind is being destroyed completely. But if you look at some hadiths, it is already happened as a miracle of Prophet Muhammed (poh).
Quran doesn't say or even imply anything about the earth's age. The 7000 thing is a belief coming from Judaism as far as I know. And again it has a place among some hadiths.
I don't know any Quranic reference about flying horses, but I heard something about 1 specific horse (Prophet Muhammed's horse) in an action like that at 1 specific time, during a miracle. And even in that saying, there is no flying, but something more like rising through dimensions (it may happen even without any kind of movement if it was real).
The creation is a different topic thou. It is mentioned directly in Quran that, humankind is multiplied from a single couple, Adam and Eve. And there is a clear mention about 6 eras of creation of the universe. Although there is absolutely no information about how long they lasted, or were they lasted equally.
So, many Muslims believe that kind of things, except flying horses, and many don't. But in the creation concept, every Muslim except a very tiny little group believe as such. This group of people interpret the creation parts in Quran as metaphores and try to unite Islamic View with the Evolutionary View, but their numbers are like a drop in the ocean.