Pretty sure it's $50 for day 4. I think I've done this recently and I vaguely recall asking the same question in person but everything's a blur and I'm tired.

There are separate phone numbers for international vs domestic valet. I can give you whichever number to call. Alternatively the email for both is the same which is [email protected] so you can email there to confirm.

I like the newer Air NZ international valet parking. I think it changed in October? I haven't compared Auckland airport valet rates though. On the to do list. There was some weird glitch when leaving the airport but I didn't encounter it and hopefully they've fixed it. I've use the Air NZ international valet maybe 2-3x since it opened and no issues when leaving so I suspect the glitch has been fixed.