Hello.
On the matter of getting an extension to reply to the CO's comments, and the adviser doing so, there's no reason as yet to think there's anything wrong. That answer will not have been looked at straight away, but will have gone to join your file, wherever it is in the CO's date-order queue, and the CO will see what the adviser said when it's next your file's turn for his attention. He will let you know if there is anything else he needs to know after he has had a chance to look it over.
A medical most often gets referred to the Medical Assessors if the doctor who did your medical ticked anywhere on the form that there was something abnormal. Did the doctor tell you at the time that anything was not in the normal range, or that you had something in your medical history that he had to indicate? And although there is nothing in the official instructions to say so, we think that there are probably certain illnesses or accidents which, if a person had them in the past, even though they are better now, trigger referral to the MAs also.
It's the MAs' job to check such cases, to say whether whatever it is is likely to be seriously expensive to treat in the future, or not. To do that, they can require you to provide letters from your doctor, or a specialist, and/or more test results - whatever will help them understand the situation. Every time a reply goes back to them, it takes at least three weeks normally for a response.
There's nothing to be done to hurry the MAs - they are a separate department from INZ, and the COs can't do anything other than wait for their clearance, either. The point the MAs are checking is that nobody is likely to cost the NZ health service too much for an existing condition. Any extra reports or tests they ask for are aiming for the answer to that question. So you may be able to short-circuit things by getting your GP (or any specialist who has seen you for anything) to write a report on you, saying (it is to be hoped) a good prognosis for your condition(s), that you've been prescribed x, and it has been maintaining your health at an acceptable working level for y years, etc., either and send it to be forwarded to the MA, or to have in hand ready for when the MA asks.