I have an old Galaxy Note 3 which supports HDMI out via MHL. I'm wondering if it's possible to turn it into a set top box by installing Android TV on it somehow. I like the Android TV UI of my Nexus Player and thought this would be a good way to re-purpose an old phone.
You can install the Leanback Launcher from APKMirror which gives you the home screen and lets you launch the Android TV versions of apps. That's as close as you're going to get though.
I installed the lean back launcher on my nexus 6 and connected the adt-1 controller to it. Tried launching a few apps that i sideloaded from adt-1 but they crashed.
No
Yes it can be possible, but no, not easily. Androidtv is a modified version of lollipop so it's like a rom that has to be ported. And unless you have lots of free time and knowledge of how to port roms, or you gather a large group of people that want androidtv ported to that particular phone and convince a dev to port it, I wouldn't count on it.