When I first arrived in NZ, I had children aged six and three, and knew no-one. I didn't know you HAD to sign children up for kindy by their second birthday, I didn't know I was supposed to take the younger one to Plunket. I thought Plunket was a place, but it didn't seem to feature on the maps. Plunket, for all you new arrivals, is what we in England would call the Baby Clinic. It's where babies get weighed, preschoolers do their immunisation schedule and developmental checks, and it's a wonderful resource for meeting other parents and sharing ideas. Often coffee groups are affiliated with Plunket. In case you're wondering about the name, it's all to do with Sir Frederick Truby King and Lord Plunket, but you can read all about that elsewhere
When you take a child into a shop, library or even bank, a staff member will often smile at your child and say "Do you want a stamp?" This has nothing to do with dividend savings stamps like the Green Shield or Co-op ones they have in the UK, nor postage stamps. Stamps are inked pictures of dinosaurs, stars, teddy bears, etc. that are "stamped" on the back of the child's hand. In the library you will often see Kiwi children standing at the counter with their hand thrust towards you in a downward fist-style. This is your cue to offer them a stamp.
Cut lunches - by definition all sandwiches are cut, although admittedly rolls, bagels and croissants may not be. A cut lunch is what a Pom would call a "packed lunch" - ie. something featuring bread and filling, some fruit and perhaps a sweet treat, though these are much frowned upon now, and lay off the chips (crisps) if you don't want a stern warning from your child's teacher and a visit from the Health Police. Cheerios (small saveloys) however are acceptable, despite having a higher fat content than chips. Again, Kiwi generosity means it is unlikely that you will be able to purchase meat at a butcher's or supermarket deli without your child being offered a Cheerio as a treat.