To add to the excellent advice barb gave you, also make sure you find out what primary and secondary insurances your parents have and make sure to get the POA to them, otherwise they won't talk to you even to answer general questions. Do it now while at least one of your parents can confirm their identity to the insurance company on the phone. My dad was in the military, so I had to make sure DEERS (Defense Enrollment Eligibility Reporting System) had my POA as well as TriCare.
I can't think of any others to get the POA to at this time besides insurance, all doctors, the hospital and any financial institutions.
Good luck to you!