New Zealand intervened in the currency market last week and the $NZ dropped, does that mean NZ prints more money to devalue the $NZ?
A central bank/country could also intervene to prevent their currency from getting too weak, in this scenario they would sell their foreign currency reserves for their local currency and the result would be that the local currency would increase in value
That is correct. Appreciation of a currency can affect exporters. It would make their exports (which are denominated in say USD) less competitive. So a central bank usually steps in (by selling / buying foreign currency) to maintain a target exchange rate.