I completely forgot to describe my experience with CM from xda developers site and Amazon Fire 7" tablet. So here it goes.
I replaced Amazon OS with CM around January of 2017 and so far I could not be happier with the device. It made tablet faster, battery life is improved since Amazon running all kinds of apps on the background and you can't shut them down. It is a completely different device with the new OS.
The CM is very close to stock Android but better in my opinion. It has privacy controls where one can prevent apps from accessing various functions with great precision. Google play store with GMS (Google apps) can be installed painlessly, making this tablet in to a low cost and usable tablet.
If one wold browse the forums, one quickly discovers that a lot of people would install Google play store on to Amazon Fire without rooting it. This allows to install apps from Google store but Amazon apps are still present, taking memory, CPU and battery life. Rooting and completely replacing Amazon software is the way to go in my opinion.
I use the tablet as my main reading device now as one can install Kindle app or any other app for reading books. FBreader is my favorite. There are plenty of DRM free book sources and even protected books can be used with appropriate readers. You are no longer limited to Amazon's ecosystem. Tablet is also OK for browsing but battery runs down relatively fast in that case. Still the tablet is very usable for browsing and especially email.
Playing music using Bluetooth headphones works very well. I mostly use it for listening to podcasts while doing housework. The range about 12 meters and after that sound is breaking up. Battery life is excellent when playing music.
I have a few simple games on it, nothing fancy, mostly puzzle games and it works well for that. I really cant say how more complex games would perform on this table since I have never tried them.
Over all I am quite happy with the device and would recommend it if OS can be replaced. For the price it is hard to beat. Unfortunately the new version of Fire OS was not rooted yet so unless that happens I would stay away from that tablet.