Re #1, there is but not sure the amount, as it was rolled into our ferry tickets. Cash was not needed. It's not like the BVI where you go to the separate window and pay it. It was included in the (in our case) CC purchase of the tickets. You will need a few bucks for "the bag man" though, if you want your bags to get (thrown) onto the ferry. Don't worry, he'll remind you ;-)

#2, you mean getting off the ferry and going to C&I, or are you talking about entering on a private boat? The way you said "checking in" threw me. If you mean coming off the ferry, no, C&I wouldn't charge any money unless you were bringing in something they put duty on. There's no fee per se.

Re #3, BVI departure tax via ferry was $20/pp cash, paid at the separate counter.

#4, no idea, but if there is such a thing you paid it when you bought your air ticket. You won't get hit up for cash at STT unless you hire a porter or unless you want to eat something.