Reading about the treasure fleet is wild:

The Chinese expeditionary fleet was heavily militarized and carried great amounts of treasures, which served to project Chinese power and wealth to the known world. They brought back many foreign ambassadors whose kings and rulers were willing to declare themselves tributaries of China. During the course of the voyages, they destroyed Chen Zuyi's pirate fleet at Palembang, captured the Sinhalese Kotte kingdom of King Alakeshvara, and defeated the forces of the Semudera pretender Sekandar in northern Sumatra.

Sounds like a fantasy novel.

IRC the genetics don't support that. It looks more like Polynesians originate from the area around Taiwan, sharing DNA with the indigenous Taiwanese. Again IRC there are some South American genes present in the Easter Island or Tahiti area, which seem to have been introduced pre-European contact. It's tricky to tell though because there has been so much sharing of genetics since then. It looks like maybe some Polynesians went to South America one or a few times and returned.

1 and 2 I think have pretty good consensus. The Bering land bridge opened about 10,000 years ago while the Polynesians didn't reach Hawaii until 900 ad, so if they got to South America it was probably after that. There is some speculation that some separate group of people crossed over even before them since evidence shows that the south American coast became populated very quickly after the Bering bridge opened. Like they got to South America before they got to the interior of north America. That could be because the Rockies are large and without the fish that those people were probably eating, or it could be that some very early people, millennium before the Polynesians domesticated coconuts, made the crossing. That theory of very far in the realm of speculation but it's a fun theory.