They are markedly impacted by acts of Congress. A number of years ago, Congress put into the Tax Code a provision that gave companies a tax break if they established manufacturing in Puerto Rico (Section 936) and a lot of pharmaceutical and medical device manufacturing moved there. These were decent paying jobs and helped the country financially. However, when the tax break was eliminated the jobs all left, many moving to low tax Ireland.
Not true. If you are a US citizen you can indeed vote in the state of your last residence. My sister has lived in Israel since 1973 but is a US citizen and eligible to vote in elections via a California absentee ballot. Her old home address counts as the domicile. In addition, you 'could' move to Puerto Rico and not have to pay US tax any longer!!!
I am aware of that tax break code, but was it just for federal taxes or were companies exempt from PR taxes as well? I would assume just the former.
Insofar as voting, your example is a little different. Your sister left the country altogether and uses an absentee ballot. However, to best of my knowledge, this is not how it works if you move to PR. Once you become a legal resident of the island, you can no longer vote in national elections. However, if you move out of PR, assuming you are a citizen, you can vote (again).
First time I heard of not paying US taxes. Is this really the case? If you move out of the country, you still need to pay US taxes; kind of odd you avoid doing so in PR.