Hello! I am one of the authors of a game engine called the OHRRPGCE (Official Hamster Republic RPG Construction Engine). It has an Android port, and it works on OUYA consoles with controller support, so I think I can make it work on Fire TV with only minimal modifications, but since I have not purchased a Fire TV yet, I was hoping somebody here could test for me and let me know how it works. There are already 2 apps in Amazon's app store that use the OHRRPGCE engine, one named "C.Kane" by Super Walrus Games, and one named "Motrya" by JSH Gaming. Both of those cost $0.99, so if somebody is willing to help me test, but not willing to pay, you can try "Walthros" on the google play store, which is also made with the OHRRPGCE engine, but just not uploaded to Amazon. (I also have the .apk file, but it looks like I can't directly link it here?) I suspect that most things should just work nicely on Fire TV, except that the on-screen controls for Phone/Tablet mode will probably still be visible. I still have to figure out how to detect when running on a FireTV and hide them.
Not 100% sure, but I think yes. As I dont know what do you mean by on screen touch controls. Like in Motrya, I see the circles in bottom right of the screens and those blinks when ever I press A or X buttons of game controller.