Most of the stores in Charlotte and Havensight are open once the cruise ship passengers are disembarking, and most of them will start closing once the passengers start returning to the ships - around 4-ish. Other than food/post office/banks that are open daily most of the souvenir shops work around a ship schedule, no ship, no open.

As for parking, obey the signs, I think you can park in Havensight for 2-3hrs (free), but there are plenty of signs to let you know.

If you're leaving Havensight for Frenchtown you take the main road all the way through Charlotte, as if you were going towards the airport. You'll pass a post office on your left, at those lights take a left into Frenchtown. It's much smaller than Havensight, and parking can be tight. Frenchtown is good for restaurants, which are always open- but I wouldn't go there for shopping - there's a flower shop, and a clothing store...

You can continue down to Crown Bay (the other cruise ship stop, continue past Frenchtown), there's a lot of shopping there, tons of parking, and I don't believe they time your parking.

In general, hours are 9-5 Monday through Saturday, close a bit earlier Sunday. When ships stay in port later, shops are open a bit longer. If there are no ships, many stores in Havensight will be closed. But if there is some specific place you want, you should call when you get here. Lots of businesses operate on unique hours.

There is also shopping in town (Charlotte Amalie), but it is a long way to Charlotte, North Carolina! 😉