Just a little follow up on your recap.
You don't need a Firestick or other device if your smart TV has the Amazon prime app on it. Just look at the smart TV features. You also don't need a plug in device if watching using HDMI cable to computer, tablet or phone. Just change the TV input to the input you are plugged into.
If you can download on a computer or tablet or phone movies when you have good WiFi, then you can watch them even without WiFi. You do need a way to connect the device to your TV - HDMI cord is the way to go. A tablet or phone needs an adapter, a PC should have an HDMI port or needs an adapter.
I download a few movies to my tablet even if boondocking, just lay in bed late at night and watch from the screen, assuming nothing else to do.