The Fruit

Question: I am a fruit. Remove my first letter, it's a crime. Remove my first and last letter, it's a kind of music. What do you think am I?

Question: What tastes better than it smells?

Question: What goes in the water black and comes out red?

Question: What loses its head in the morning and gets it back at night?

Question: What two things can you never eat for breakfast?

Question: What asks but never answers?