1. Dilion is not a police officer, he is a famous detective a private one. He is there because his friend (The Count Lovelle) asked for his help with something. I didn't pointed that out in the demo, woops :'3
The Count gave him the emblem for the time he is there.
2. Yes, Just because the count told the guards to follow his orders.
2-1. Dilion doesn't use formal words to talk to other police officers.
I think "Sir" would be more accurate, since "Mr." Is used before the last name and Dilion is his name. Also "Sir" is more formal than "Mr." Which is the case here.
And, sure! You're free to do it! :D