Im trying to figure this out myself. I have a rooted firetv 2 but rn it may be bricked waiting on usb cord to try to fix it. If i do ill let you know for sure. Doing a search last night there is a reddit thread where someone dumped fire tv apks that worked on Android tv was 2 yrs ago. I downloaded sci go and it didnt work actually made my screen get stuck and only cuz i have a shortcut button for settings was able to uninstall to fix it. So if i fix my fire tv i will let you know the results. Usb should be here tomorrow or sat.

Yeah it's possible. I'd grab the apk for you but it's restricted to USA and I can't be bothered to change my amazon account. There are various ways to get the apk off amazon devices.

Usually but not always. Sometimes there's a hook in the app that requires the Amazon app store to be installed. Other times there's functionality that isn't available on the other platform. Other times an app might look at the build prop to make sure it's running on an Amazon device. Most work fine though

Yes, maybe, but it's a bit complicated. You basically have to download the app on a Fire Stick, export the APK, sideload the APK and the Amazon App Store on your Android TV, install Sideload Launcher, use that to launch the Amazon App Store, log in to your Amazon account, and then finally open the app up (you might need to use Sideload Launcher for that as well). And even then, there may be core functionality that doesn't work on Android TV; for example, I tried to load the TCM Fire TV app on my Shield, and provider login didn't work.

If it's a popular app, you might be able to find modded APKs on XDA or another enthusiast site that have had the Amazon DRM check removed, which makes things much simpler.