A few questions after my first viewing

In no particular order:

1. What is the reasoning behind the custom of painting the teeth black?
2. The scene where she runs away and goes back to the mountain and finds everyone's gone. She wakes up back in the palace with the broken shell. Was that a dream sequence?
3. The flying sequence; was that also a dream sequence? If not, how did she get back from falling into the sea?
4. Her old friend whom she loved; he was married and had a child. Was it ok to say he'd run away with Princess Kaguya. How are we supposed to view him if he's willing to abandon his current family. Or am I missing something in japanese culture?