I am the only organ that named myself

Question: I am the only organ that named myself.What am I?

Question: My thickness is no more than a few centimeters, yet my depth can span to infinity. Although mundane, I intimidate most animals. When in my presence, you will inevitably follow me. What 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?