Kindles on the same account can share books, which would make sense for your parents. They can't share subscriptions, however, so if they both want to read the New York Times (for example) they would either need two subscriptions or share the Kindle that has the paper.
You just have to have one Amazon account that all the Kindles are registered to. For example, I have four Kindles on my account -- my two children and a friend. All the content in your media library can be shared among the Kindles on your account. It's very easy.
Keep in mind that someone's credit card is on the account -- in my case, mine. So when anyone buys anything, I get charged. This has not been a problem for me but again, just something to be aware of.
If a person was outside of the US, they would not be able to use the Whispernet to acquire books through the content manager. So, that person would need to know the user ID and password on the Amazon account where the Kindle is registered. Then s/he could log into the account, download the books to his/her computer, and transfer to the Kindle with the USB cable. Thinking this through, I don't see any reason why it shouldn't work.
Be aware, though, that the person has access to the Amazon account with all the credit card info, etc. Remember I said above, I have my children and my friend on my account? I do but none of them know my id and password, so they can't get into my account on their computers. They can only get books and things using the Whispernet on their Kindles.
Alternatively, a friend and I share the same Amazon account for our Kindles. We trust one another to see our credit card information. And, we just switch the default credit card for the account back and forth when we make purchases (it's very easy to do).