Wish I could help with specifics, but to be honest I have encountered so many issues with puppets in the past that I entirely discount them. I gave up trying to figure out what the problems were. To the extent that I try to avoid puppets altogether, I just annex everything whenever I can. The exception being Ethiopia. Because who wants to garrison Ethiopia?
Even when you start with puppets I found I could encounter situations that seemed to defy any sense. I assume its just a bug. For example Russia starts with two puppets. One of them, Mongolia, iirc, showed an excess of supplies. Something like 30. So I traded them for 20. Done deal. Continuous border. No wars going on. Only the screen showed the trade as inactive "Not enough supplies". But they still show an excess of 30. So I broke the trade and tried again with 10. Done deal. Only the same story. "Not enough supplies" although they still showed a solid 30 excess. A year later, yup, still the same story, even though I gave them lots of energy, steel, rares, all of which they seemed to receive. I decided it was just easier to invade Poland if I wanted free stuff.
Possibly in your case the tag switch might muck things up. I really dont know, but at a guess I would say once you tag switch the game will penalize you accordingly for not being an AI. So your production and resources as NZ/Aussie will be much lower than as when they are AI.
So in conclusion.
1) I dont know.
2) I think so, since they are now back under AI control.
3) If you are trying to boost them up as being better fighting partners I am not sure. I am guessing you would want them to pump out some nice land units and transports, rather than build an endless array of coastal forts. The AI usually makes a complete meal of things once you give it any sort of control, but you could try lining up some good stuff in their production queues, increase their officer ratio, and then tag switch a month or two later to see if they are still producing what you want them to. To add: If you are relying on them giving you expeditionary forces then good luck. I find it takes way too long, if ever, to get decent expeditionary forces out of a puppet, and the units they give are more of a liability than an asset ( the exception being late game UK which does get some useful garrison/front line forces from its Commonwealth allies, and some decent front line units from the USA )