iTunes is a stubborn program to use. Unfortunately, you cannot play a show on a different account than the one you purchased it on.
Converting videos is an entirely different matter. I remember back in 2011 that basically any converter could back-end iTunes and convert it. Recently (Last 3 years or so) Apple has updated the video codec on iTunes making it disable copying, converting and playing on unauthorized computers/devices. Only certain shows and movies are unprotected (almost none). The only way to play protected videos on a computer is by authorizing it on iTunes/Quicktime and then playing the video in a authorized video player.
So unfortunately there is no solution to this. Personally, I haven't had to deal with using iTunes and Apple software after my mother finally ditched her 2010 Macbook Air in early 2013. There could be a recent solution, I'm just not aware of it.
Quick info here:
http://www.fileinfo.com/extension/m4v