We can’t tell you how their phones will work while there, but while on wifi you can place calls and send texts to their US number, doesn’t matter where the phone actually is.
You can receive calls (and probably texts) from anyone while on wifi there. You’ll get nothing from anyone off of wifi. I say probably texts because not all foreign carriers will route international texts. If you can get their texts while in the US, you’ll be able to do so while on wifi there. If you can’t get them at home, you won’t get them there either.
You can do anything that doesn’t require a network connection. So use offline maps, read a downloaded ebook, listen to a downloaded podcast, etc.
The only thing Skype would add functionality wise is the ability to call NZ numbers while on wifi.