Good questions. Like other peoples in the Pacific the Polynesians in Hawaii largely originate in the Austronesian homeland of Taiwan around 6,000 bce. The branches that eventually became the Polynesians also intermingled with the existing Melanesian peoples in near Oceania who had begun migrating down around 40,000 years ago. So while they do originate from the old world, they split off well before the infectious diseases that would later fell them had become a threat. There were also potential population bottlenecks along the long trek between Tawaian to Hawaii which gave ample time for unnecessary immunities to be lost or to simply not be maintained.

They did raise domestic animals, but they did not live with the animals, nor were they raised in massive numbers- most had ceremonial value or status- they consumed too much in the way of resources to be raised in great quantities (though there were and always are exceptions to this). Polynesians carried the rat, chicken, dog, and pig throughout much of the Pacific. Hawaii was home to all four.

As you can imagine, a population isolated from the more dynamic disease centers of Eurasia simply lacked immunity to some pretty common (though still terrible diseases: smallpox, tuberculosis, influenza). It's also not just that people died in great numbers from introduced diseases, but STDs like syphilis also helped to suppress the birthrate, so people just weren't having enough babies to replace what was being lost.

David Stannard's "Before the Horror" is a solid, if rather confrontational overview of this. While controversial when it came out, his populations estimates and rundown of depopulation have become more widely accepted. Estimates by archeologists like Pat Kirch have slowly creeped upwards over the decades as well and aren't too far off the narrative created by Stannard. On that note, KIrch's recent work "Kuaaina kahiko" looks at some of this in interesting ways as he writes a sort of long duree history of Kahikinui on Maui.