check the website of the domestic carrier for baggage restrictions. You cannot carry anything fluid in your carry-on, and this includes tooth paste to some. No wine, no drinks, no hair stuff.. nothing.

i found european baggage restrictions less than north american... dunno about NZ vs US

you always have to collect your bags to go through customs... so they can check them if they want. Generally you hand them right back to an airline thingy if you're going right onto another flight though.. but that depends on the time b/w flights. Most airlines wont accept responsibility for baggage more than 2-3 hrs before a flight. We had to sit with ours all night once

4-5 hrs sounds safe.