On the car hire question, most of the car hire companies will allow you to hire a car from Auckland, drive to Wellington, leave the car, get the ferry as a foot passenger, and then pick up another car at Picton.
We did something quite similar to you a couple of years ago on holiday. We flew into Auckland on ANZ, spent a few days in Northland, went back to Auckland and flew down to Queenstown then drove back up the South Island to Picton, dropped the car off, took the ferry to Wellington, picked another car up at Wellinton and made our way up to Auckland again to catch the flight home. The car hire compny (Apex) counted all the hire as one, even the first few days in Northland so the price per day dropped quite significantly.
I booked the internal flight in NZ from the UK on the NZ website with no problems, also the ferry as well.