Do you need to schedule your date and time ahead of time or is it ok to wait until the week you're in Charleston and book it?

I think you'd be ok to wait depending on the season however I recommend scheduling. When I scheduled though I know you can pick a date as a guess and it will show you how booked other dates are, I also think they may be flexible to changes under their ticket terms.

Absolutely not. You can buy tickets right before the ship boards.

No we arrived and were able to get on a tour within 15 minutes

I go tour pretty often we have dropins I go down and book then or on the next tour.