I think you would be better to ask for an IQA. PAR can't be relied on to be correct.
PAR is only ever done by a look over the names of qualifications - what they're called by the awarding institution in the other country - so it's not necessarily exact, since terminology doesn't always have the same meanings in the other culture and in NZ. IQA is done by an in-depth look at what was studied, for how long, to what depth, and then comparing that proof with what is done in courses within in NZ, to find one NZ qualification (if possible) that they can say it is nearly equivalent to.
On the threads, we have seen where people's Level has gone up, OR down, between PAR and IQA, since PAR only depends on what words happen to be in the name of the qualification.
So you may possibly find that you have the extra points you need.
For proof of English for your wife, yes, she will need to write to her university to get a letter stating that she (by name and age) attended there on (whatever) course, between this date and that date, and that the course was delivered all in English. (Even when English medium is mentioned on the transcript or certificate, such a letter is still required separately.)
What is your career? This will make a difference to what can be considered by INZ as your qualifications for the job.