I'll try to answer your questions to the best of my knowledge.
To start with though, a question for you; Do you have permanent residency in NZ? Without this you will struggle to find someone willing to employ you. I'm not talking about being able to get it, you need the paper in your hand.
250 hours in aeroplanes as PIC including 100 hours of cross-country navigation of which 25 hours is to have been at night. Does General Aviation PIC count toward this?
Yes, GA time counts. All that matters is that you were PiC and not under PICUS (command practice etc) or under dual instruction.
IIRC, if you meet this requirement, you do not need to worry about the other two requirements. From memory, there is an important OR included in the AC (I don't have it in front of me).
On the medical side of things, there is a directory of medical examiners on the CAA website under "medical", including some overseas. Find one near you, pay the CAA fee, fill out the paperwork, and you're good to go. Expect to pay well over $500 total for a straightforward medical, once all the fees and charges are accounted for. It could be a lot more as well depending on your circumstances.
There is a book published by waypoints aviation for the law exam. This contains the "raw data" you will need to know for the exam, plus some practice exams. I think there's also an ATPL online course.
As for a sim ride, it would depend on what type of aircraft you are looking to do one on. Best bet is to find the sim, then find out who can arrange it for you, and try to get in touch.
As to what time is best, I'm not really in a position to comment. Air NZ is the largest employer in the country by a large margin, for turboprop and jet operations. Their careers website has their requirements etc. There are other threads running on here about the chances of applicants at the moment. Failing that, there are other operators out there, your best bet would be to phone around and see what they are looking for.
Good luck!