Hello Luane,
Addressing Point 3:
When Me and Bunstar first arrived we were travelling round the North Island in a Campervan, but I had set up 'Skype' on our laptop P.C. which we brought in our hand luggage, and our folks back in Manchester U.K. also had Skype set up in their P.C.'s. We found that we could video call back to the U.K. via Wi-Fi from campsites over here, in fact the first question on arrival at a new campsite was generally 'do you have Wi-Fi?'. Even with 'pay as you go' style Wi-Fi access, video calling in this way was very reasonable, but of course you need a laptop P.C. in the first place.
The main reason for the laptop for me brings me to your Point 2, job-hunting. A quick search on
New Zealand YELLOW? for employment agencies or suitable areas of employment in the local area will usually generate a good list of doors to knock on to keep you busy for the next day or two. I bought a cheap local mobile phone and updated my C.V. with the number as a couple of agencies seemed less than keen to call me on my U.K. mobile phone. Maybe it was the call cost to them, or maybe I just looked more commited to them with a local number on my C.V., I don't know, just an observation.
This yellow search followed by door-knocking certainly worked for me in Engineering, but your field of work may require a different approach, (Priority One, or NZ Herald perhaps). Good Luck anyway.