When you had your medical, the examining doctor must have found some results which were abnormal. If ever the doctor ticks the 'abnormal' box, the CO must refer the medical to the Medical Assessors (MAs). The MAs are in a separate department. They have medical knowledge. Their job is to make sure as far as possible that nobody comes to live in NZ with an existing medical condition, the treatment of which would be likely to cost the NZ Health service more than NZ$41,000.
http://www.immigration.govt.nz/opsmanual/45634.htm The MA has asked for these tests so as to check this about your health.
The CO is not able to finalize any case and issue a visa until the MA says the medical is passable.
The tests the MA has asked for regard your blood sugar levels, and the function of your kidneys, liver and heart. It may be that there were false readings at your original medical, for instance, if you had eaten a very large meal, or you had taken concentrated exercise, in the few days immediately beforehand. In that case, further tests will show your functions as normal (only be careful to eat and exercise only moderately for a week before). On the other hand, you may already know you have some health problems, and in that case, there should be doctors already taking care of you. If you DON'T know of any problems, the next step should be to see a doctor to be referred for the tests, and, more importantly, so he can give you advice about taking care of yourself.
The MA will want the results of the tests, and, if any are abnormal, will want a doctor's assessment of your condition, what treatment is necessary, and what the likely outcome is over what period of time. If you don't know of any condition yet and abnormal readings at the medical are the first sign, then for the sake of your health, the best thing to do is to get some treatment started as soon as possible, without waiting for any other comment from the MA. Then at least, your doctor will be able to write a letter for the MA saying what he has found, what treatment has been started, and what the result has been already, in the (say) four weeks from the first appointment till the next reply from the MA.
English requirement for your wife. Since you mention recognizing your wife's qualification, I guess you are using some points from her to meet your total? In order to get these points, the partner's English has to be at the same level as a principle applicant's, that is 6.5.
http://www.immigration.govt.nz/opsmanual/42640.htm
You say this. And yes, I think that is your next step. Notice that the CO
may still ask for an IELTS score, but would have to show a reason, and would have to allow time for this to be done.