score:4
i) will my application be rejected if I submit the documents completed by my general practitioner?
The wording of the application form includes the word "must" which indicates that in your case, applying from the USA, where there are 22 panel physicians in the continental USA, that yes you must use one of these physicians to carry out your medical.
ii) in case Immigration New Zealand does not accept my general practitioner's certificates, will they ask me to update the certificates rather then rejecting me?
This is a good question - in the case where we got my wifes employment contract wrong, NZ Immigration didn't throw out her application but instead contacted us, explained what was wrong and what it needed amending to, and allowed us to amend the application with the updated documents.
So you might get the same thing - however, I cannot find any public guidance on this, so other than experience it will be hard to answer...
iii) is there an authority that I can consult on the matter?
Yes, you can talk to New Zealand Immigration and ask them directly - I have had reason to contact them several times in the past 2 years and they have been extremely helpful and supplied direct, useful answers to my questions.