Where do the cruise ships dock, and what all is there to do and where is that in relation to Belize City?
The cruise ships lay anchor off shore. People are brought into the cruise ship terminal which is in front of where San Pedro express water taxi docks. The terminal has restricted access to only cruise ship passengers. It is full of drink spots and duty free stores who can really only sell to cruise ship passengers.
If you show your passport you can get in, but you are not allowed duty free stuff just food and drink. Fairly expensive food and drink but it's interesting.
Norwegian Cruise Lines has their own pier offshore on Harvest Caye south of Placencia as well.
Are cruise ship passengers allowed to leave the area to walk to the Belize sign there on the water?
Yes you see lots of cruiser peeps walking around and taking in land tours. They have horse drawn carriages. The sign is a few hundred yards east and an easy walk.