Bigger issue than voltage (easy to resolve), frequency (should not matter in this case), is the TV standard. US sets are designed to operate using the NTSC standard, NZ uses PAL. not 100% positive but this may be the showstopper for you.
Not an issue. The OP plans to use only the HDMI input, nothing over the air.
Not an issue. The OP plans to use only the HDMI input, nothing over the air.
Larry
I believe you are right Larry after more research, using HDMI will work fine also no problems using the Wifi, will be buying a Pure Sine Wave inverter rather then a Modified Sine Wave.