I can't answer all of your questions, being Canadian, but I can give you a start on a few things:
1. When we flew in from New York, we used LAN (a South American airline) that had good service & nice amenities, even in coach. The airline flew directly in to Guayaquil.
2. There are a lot of things to consider when choosing where you want to stay. The larger cities along the coast will have more amenities (meaning hospitals and medical services) and be easier to navigate if someone has trouble walking. Be prepared for poorly maintained, missing or uneven sidewalks, wherever you decide to stay. Salinas, Manta and Esmeraldas are the large towns/cities on the coast. As far as I know they are all open to the ocean breezes, but depending on the time of year, can be really humid and hot.
3. I have no idea about Medicare Advantage, you should refer to your government information package on out of country service.
4. There are car rental agencies in Ecuador, especially in the larger cities. The roads, for the most part, are narrow, winding, poorly signed where defensive driving is a must. The roads can be dangerous in the day, depending on the route, just because of the large vehicles on tiny roads and drivers that aren't the best. (Lines on the road are barely suggestions, lights can be ignored and drivers are, at best, unpredictable. Many North Americans avoid driving me at night, as most of the roads are also poorly lit (or lights are non-existent). Many opt to hire drivers to get them from place to place. I do know North American's who drive here and we will once we get our Ecuadorian drivers' licences, but we only plan to rent for the odd road trip.
5. The easiest way to deal with money here is bank machines. An ATM card/Credit Card can be your best friend to get cash out of a bank machine. Cash is king here, credit cards are only accepted at large stores, major hotels and high end restaurants. I would bring a couple of options, just in case one card doesn't work, for any strange and unknown reason. (Networks being down, strips demagnetized etc.) If you are planning on staying in a small town, you'll likely have to plan ahead and carry cash with you. Most banks have security guards at their front door, near the ATMs, so we haven't had a problem so far.
6. You can enter Ecuador for 90 days on your US Passport, longer stays will require that you apply for a 180 day tourist Visa or an extension on your original 90 day...this can be challenging if your Spanish isn't up to snuff and you don't want to shell out money for a lawyer, or "handler" to act as a liaison between you and the government.
Hope this helps somewhat. Good luck!
5.