Is there a place to park when picking someone up that is arriving on a incoming flight?

Yes, there is a small lot just down the road from the airport labeled "Cell Phone Lot". You can wait there until you get a call that your party is at the arrival level or is ready for you. It's just off SR-237 South and there are blue signs directing to it. It's also free.

Yes but you have to pay. It is best just to be there when they call so you will not get sited for standing idle in the car waiting.