Barbara, this page (click HERE
) should address most of your questions. Parking is $24 per day, but I notice that a monthly rate of $180 is available for 8 days or more that's worth looking into. Hopefully, someone here can chime in on that one.
The main site for the NY Passenger Ship Terminal is http://www.nypst.com/
...the link I provided above goes directly to the parking section, yet there is a lot of great information accessible from the main site.