Question: questions to ask your best friend how well do you know me?
Answer: What embarrasses you the most and/or what's been your most embarrassing moment?
Who do you look up to the most, and what qualities do you love about that person?
What would be your perfect day? ... 
What's your biggest fear?
How do you like to be comforted when you're sad or upset?
What's your all-time favorite memory?