Feed refresh control would be a setting to control how long the interval is for the feed to autorefresh showing new posts. If a setting could be added for the user to set his own time in minutes & the option to disable it making the feed refresh only when you swipe down from the top manually. I believe that would be a great start.
As for the video player even when not using amethyst it is still running in the background playing the last video unless you force close the app. I'm not sure how you would implement it to stop when you go back to the homescreen or when you slide away from an video in a feed till you get to the next one. But that's probsbly why the phone always runs hot.