Afaik, Northern Ireland is less autonomous than Scotland, so I don't know why they're that way round, and that's the flag of Eire / The Republic of Ireland, not Northern Ireland, which isn't (currently) part of it, it's part of the United Kingdom. It's inconsistent to use the Union Jack on Scotland Wales and England but not Northern Ireland, and its factually incorrect to use the flag of Ireland on it.

Puerto Rico is an associated state. It’s in the name — Estado Libre Asociado de Puerto Rico.