New Zealand is an interesting control group of sorts, having a high vaccination rate but as of yet an insignificant percentage of the population that has had the virus itself. In addition to the questions you have, I'd add that vaccine injuries are more common in those who had the infection prior to getting vaccinated, so you could be having a lower rate of adverse events because of having fewer people in that situation.

It's still early in the game for the long term effects of the Vac and interactions between the Vac and the virus, especially for NZ, so we'll just have to wait and see.