"What is your management style: hands on, or hands off?" Basically you're trying to figure out if they are a micromanager, or if they will treat you like a professional and let you do your job without too much fuss.
"What do you think is your best quality as an employee?" You're asking this to see what sort of quality they tend to respect more in their employees.
"How do you resolve conflicts within your team?" Basically you're trying to see if your potential manager will wimp out at the first sign of trouble or not.
"How would you expect your team to resolve issues and conflicts?" You're asking how they expect the team to function in a crisis.
"Where do you see yourself in 5 years?" Figure out if they are ambitious or not, and possibly if they'll step on you or use you to get themselves ahead.
"What is something you struggle with professionally?" You're trying to see if they have enough self awareness to meet your needs. If you don't care, then don't ask.