I think I may have answered a similar question before, but I can't find it so you can have a brand new one.

The Polynesian explorers are often trumpeted in New Zealand and the Pacific as the greatest seafarers in history. It's a hard point to debate. As you've correctly pointed out, they did it across thousands of miles, and with a high rate of success. They also did it before the advent of modern navigational tools, guiding themselves by the stars, currents, and winds, and with generations of knowledge amassed in their oral tradition.

So what did this knowledge include?

Firstly, the techniques of how they found new islands. There was no knowledge of what lay beyond the horizon, but the explorers devised a practice where they would go from their homes into the direction of the winds and currents, making distance until they had used half their food and water supply. When they reached this point without finding land, they could turn back, sail with the wind and current driving them forward, and easily reach home. This strategy was repeated across the Pacific, allowing the seafarers to go into the unknown in repeated fan shapes (imagine several curved lines coming out from a single line, but all going in one general direction east/west - sort of like an outstretched palm with five fingers) and cover wide areas of ocean. In this way the majority of the islands in the Pacific were discovered. When Captain Cook came to the Pacific he had a Tahitian guide, Tupaia, on board, and Tupaia was able to map large areas of the Pacific despite only having visited a small number of islands. This was because the knowledge of the other islands was recorded in the oral tradition and passed down to the new navigators.

Another key part of navigation was knowing the ocean and the movements of its inhabitants. There are seabirds which (ironically) won't swim in the sea, and will stay home, others which migrate at different times of year, others which fish during the day but roost at home on land. Knowing these species gave sailors an extra bit of guidance if they saw them. Like European, Polynesians also used the stars to navigate, giving them bearings for directions home, and to new islands when they returned home to collect settlers.

So in some part it was luck - they didn't know what was out there, but they tested it. And in that regard we see how the claim of greatest seafarers gets a bit of backing to it. They weren't sailing with modern trappings, but with their knowledge of the ocean from previous sailors, and with a great deal of ingenuity and intelligence about the ocean and how it worked.

To your other questions. I don't know about the attrition rate, and how many died at sea, but there must have been some who were caught in storms or lost their way.

Contact with South America has been suggested, particularly with some crops appearing in New Zealand which are common in South America, as well as (I think) chicken bones from the Pacific being found in an archaeological site in South America.

I don't know that any went to East Asia, but the Polynesian peoples are believed to have come from Taiwan originally, sailing East into the ocean, so it could be assumed that there was knowledge of a previous land but I've not heard of any proof either way.

And a final note for any readers on the differences between Polynesians and Māori - the indigenous people of New Zealand are Māori, who are a distinct group of Polynesians. Polynesians became Māori when they settled New Zealand and a new culture emerged.