I am flying to Brisbane tomorrow from Ronald Reagan Washington National Airport (DCA) to Houston, then on to Auckland (7 hours there), then to Brisbane. I am planning to exit the airport in Auckland to see friends in Auckland. Do I have to offload all my baggage in Auckland, then check in again? I am assuming so, but can I check in baggage immediately, or do I have to wait until 3 hours before the Brisbane flight?
Whether or not you need to collect your bags on an extended connection will depend on the airline. Some have rules that more than X hours (where X could be as few as 6-8 hours, but is normally more like 12 hours), or a connection that is overnight, will require you to collect and re-check your bags. Other airlines will not require you to collect them for a stay of less than 24 hours.
For 7 hours it is extremely unlikely that you will need to collect your bags. This is well within the timeframe that they will be automatically transferred for you on a connection like this.
Note that as of October 1, 2019, in order to do what you are suggesting you will need to obtain an NZeTA and pay the International Visitor Conservation and Tourism Levy (IVL) - at a total of just under NZ$50. If you were simply in transit (ie, not entering the country) you would still need the NZeTA, but will not need to pay the IVL, bringing the cost down to around NZ$10. (If you're an NZ/Australian citizen you don't need to pay these fees, but basically all other travelers will)