i have a few things that i don't quite understand, i need help...

here are a few questions:
1. was Mohammed really married to a 9 tahun old (i've heard this and i don't want to believe it because that would change everything for me)?
2. is it true that Mohammed's Daughter Fatimah was married to Ali, Mohammed's cousin (i mean that makes it incest, i know Quran is against incest because it's wrong and disgusting)?