Absolutely it will cover you. Auto insurance is designed to protect you in any circumstances that occur when you are operating your vehichle. And since you were driving the car when it happens yes the pedestrian can file a claim against you.
It depends on the terms of your car insurance. If you have the proper coverage you will be covered for the injuries the pedestrian sustained up to a certain amount.
If you have full auto and liability coverage, yes. If you only have collision insurance on the car (which only covers the car if it is totaled), then no. Read your policy to see what coverage you have.
Your insurance will pay for their medical and repairs to your car, but if criminal charges are filed, then your insurance does not assist with this unless clearly stipulated.
