Can I change the date or the number of people?
Ask as early as you can. Changes are the captain's decision, since they depend on the boat being free and the group still fitting within its limits.
Moving a date is usually straightforward if the captain has the new day open. Changing group size can affect the price — on a private charter it often does not, since you have taken the whole boat, but on per-person trips it will.
Adding people can run into the boat's maximum capacity, which is a legal limit and not something a captain can stretch. Ask before you promise anyone a place.