If you don't have a Smart TV, Chromecast or Amazon Fire Stick will both work. I have all three (Smart TV, Chromecast, Amazon Fire Stick) and can't tell a difference when streaming (which is the only way I watch TV).
Different companies have different casting. Android software has chromecasting built in. Samsung liked to use Allcast.
There's a 0.1% chance you can download Allcast and get it to work, but I really doubt. Easiest is have amazon ship you a chromecast.
I have an Apple TV 4 and a Amazon fire tv with kodi. Canceled Directv and saving $140 a month.
Not sure what the issue really is. Is it a Droid Turbo by any chance? Those things are notorious for screen casting issues.
Nope, Moto Z. Motorolas are not listed as compatible on the Samsung website.
As to the question of the ESPN app: Yes, my XBox has the app, but it isn't the same. It doesn't have all the replay games available for some reason. I don't understand why they are different, as it still logs in through my TDS account.