Do you have to remarry in the US after you got married in Asia with an American?
You can marry anywhere.
If an Indian get married to an American in US to get a PIO should they remarry in India or is the marriage in US valid in India as well?
If your spouse was legally married in another country when you married and then gets a divorce in the other country should you remarry in the US?
Marriage laws are determined by your state of residence. Most states follow the general rules that if your marriage was legal in the place you got married, it is legal and valid in other states/countries too. If you were married in Guatemala and the marriage was valid there, you will have to get a divorce before you can remarry. You can divorce in the state where you now live.