I can only help with the parking question. There is a pay lot in the center of town, a couple of blocks behind the old courthouse. There is also free parking a couple of streets further back but it often fills up quickly. There is also a pay lot near Chesterfield's as you are heading towards the cruise ship pier. If you eat at Chesterfield's they were validating your parking for the first 2 hours.

You are correct, there will more places open and probably longer hours on a day a ship or ships are in port.

Have fun!