We took a taxi from our hotel to the port, so I can't help you with respect to parking at the pier.
As far as boarding goes, we intended to arrive at the pier by 11am, but were told at our hotel that boarding was delayed due to icy conditions on the pier which caused the delay of the disembarkation of those passengers leaving the Galaxy. I'd say we were on the ship by 12:15 - 12:30, and were amongst the earliest arrivees. Our taxi waited in a relatively short line to enter the pier, at which time we had to show picture ID. We were then directed to a tent where we dropped our baggage and were taken by van to the ship (perhaps the distance of a block from the luggage dropoff point).
We were the first group to disembark (combination Captain's Club and early flight) and were off the ship by 8:10am. This was by far the easiest and fastest off procedure we've ever experienced on any cruise. We were at the airport before 9.
The weather was a bit "cool" in Charleston during our few days there prior to the cruise. In fact, it wasn't much warmer than it was at home in NJ. However, by the afternoon we boarded the ship, it had warmed up and was fine for the remainder of our trip.
Belize - We, and many fellow passengers, wondered why this port is even on the itinerary. There is a long tender ride into town (20 - 25 minutes) and you are let off in a relatively newly constructed tourist "village" (nothing more than a few shops, including a pharmacy which sells over-the-counter prescription drugs, minus the prescription!). Once you step beyond the shops you are in downtown Belize, a place few would feel safe walking around. This port is one of the poorest we've yet to visit. Downtown is awful. Prior to leaving home we booked a private tour of the city through Regtour. We spent an hour and a half driving through Belize City, which is a combination of poverty, blight and nothingness. We drove through the north side - the "wealthy" part of town, described to us as the place where the "kings and queens live" - and with the exception of the Prime Minister's home and perhaps another one or two homes, the area was depressing, to say the least. Even by moderate US standards, the best homes left much to be desired.
Several folks we met took shore excursions to the animal sanctuary, the rain forest, and Altun Ha, the Mayan ruins. No one was terribly impressed by what they saw, and everyone complained about the very long and uncomfortable bus rides to wherever they were going. Cabe tubing seems to be the only tour that was enjoyable, but even that involved a long bus ride.
Hope I've answered your questions. If you have any more, please feel free to ask and I'll do my best to answer.