This happened in one TL here. Maize grows quite well on Easter Island leading to a population boom. Unfortunately it doesn't end well since maize exhausts the soil, the greater population puts more pressure on resources, and in the end everyone dies because of famine, warfare, and kuru epidemics.
But regardless, maize on Easter Island could be helpful although the main importance would indeed be finding a way to get it to New Zealand. If the Maori get it in, say, 1400, then they'd have several centuries of exponential growth on North Island and most of South Island. The Musket Wars would be less devastating when they come since the population wouldn't have just undergone such a major expansion. I think with the larger population you'd have New Zealand consolidate into several regional "kingdoms".
It's possible that Europeans would have prolonged contact with the islands earlier, and while this means earlier disease, Europe will appreciate the larger market to sell to so visit more often. If disease and depopulation and potentially earlier introduction of the potato (still very useful on South Island) still shake up Maori society--which it will--then the Maori might get the idea to go conquering and hitch a ride on Dutch, English, or whoever's ships to Tasmania or Australia and found new settlements there, wiping out the locals with their superior tactics, fortifications, and weapons. In many ways you're transplanting the 19th century Maori back to the late 17th century or so, but they'd likely be even stronger since the Maori population still probably won't have hit carrying capacity when the epidemics arrive (although said epidemics will keep the growth rate low thanks to the high death rates of children).
TTL I don't see Europeans making New Zealand a white majority nation, since they'd at most be able to do so on South Island. If they settle New Zealand then they'd be a minority ruling over a majority Maori population. I could see that with European weapons and advisors and perhaps a conversion to Christianity, a Maori ruler might conquer at least all of North Island, and potentially part of or all of South Island too in which case they have a very good position to survive as an independent country. TTL more activity in New Zealand (a market hungry for weapons and European goods) might make it so there's a few European powers in Australia so the Maori could play the Europeans off each other and avoid becoming a protectorate. They'd likely remain a small, remote, rather impoverished island country, left alone thanks to being so far out of the way.
I have feeling they'd be the Vikings of the New World being big time coastal raiders and trader across the western coastal region of the Americas, establishing various colonies.
I don't know. On one hand, the very limited water sources (one or two springs, otherwise you basically need to collect rainwater) means Galapagos could easily centralise power on the basis of distributing water and controlling access to the resources (and people) for making fog collectors and barrels to collect rainwater. On the other hand, it's population is likely to be fairly limited so that limits the amount of warriors and people to send to establish colonies (at least colonies that won't assimilate with the locals). I think the Manteños will do it far better since they already made long-distance voyages (as far as Mexico) and with better sailing and navigation would take their trading to a whole new level.