Hello, thank you for using this service. I wish to introduce myself. I am Michael, a Research Librarian with 20+ years of experience.
Sounds like you will be a world traveler by the time you get home!
Before listing information on healthcare on these various countries, let me give you company information listings on travel health insurance you can purchase before your trip. The US State Department has a complete list to use to compare pricing
Researching tonight information on each company with links that offer clear details. Each country has it's own policies for payment so purchasing insurance would be the way to go.
As for your question on possible loosing your passport (I hope not), research first when you are in each country where your local embassy is located as they would be helpful in this matter. In fact, registering in each country you visit with your embassy can be essential if a problem does come up.