Easy fix for the grayed out install button..it is NOT an amazon app issue. You installed something that created an overlay on your screen itself which is preventing you from installing anything 3rd party or from Amazon . Things like an app called Lux and Screen Filter can do it (which do something with your screen brightness I think it is) . Check all your apps for anything that states something along the lines of creating an overlay, and remove said app, and your installs will work fine.
I had this happen to me when I used an app that kept my buttons lit up when the phone screen was on. Removed that, and cleared up my issue.
Amazon has been working for me since I got my One 2 months ago, never an issue (well except mentioned above but that was another app causing the problem)