Is there a monthly charge for this?
The fire TV stick or box? No that’s a one off purchase AFAIK. Amazon Movies is part of the Amazon Prime subscription. So yes as far as their content goes. Or u can PPV/buy what you want.
Not all movies are available through the prime subscription. Some you still PPV. They update content all e time
You can still access your own(ed) content from your network / your other devices.
I don’t have an Amazon Fire device.
Stick, box what’s the difference? Boy am I bring lazy! 
The box is more powerful, so menus will feel more fluid, apps will launch faster, and you’ll be able to play more demanding games (not sure who would want to play games on it, though).
The box can also be connected to the internet via cable, so if you’re wifi is spotty next to the TV, that might be a better option.
And, obviously, the box is bigger and more expensive.
Get a Roku box and have access to Amazon, Netflix, Google, Sky, Plex, Youtube and virtually any other streaming service you have heard of through one device.
I saw Roku I tesco. There was 4 of these things on the display but no staff to advise. Thank you
I’d just get a raspberry pi and put Kodi on it. But I’m a tinkerer.
How does Kodi on raspberry pi compare to double cream on raspberry tart or a Tiptree cream tea?
sigh you ol’ timers
Would suggest the Roku as the number one choice, unless you download yourself?
I’d suggest the Roku or something like it too