No - it is not usually a tender port. Most Hawaii ports have several options right on the pier when you get off the ship - like tours or rental cars. However, it might be a good idea (cheaper?) to get one online before you go so you know you have one ready. They might even have it at the pier for you when you arrive.
No, there are no rental agencies on the pier at Kauai, and have not been since 9/11. You need to reserve a car at the airport (about 4 miles away) and all the major companies will then run free shuttles from the pier to the airport. We have had good success using Alamo there. Be sure you have reservations (which you can book on-line).