Bought the iPhone 7 battery case last month and so far so good! Feels great in the hand and can get me through two days. Headphones work fine and charging both the iPhone and the case simultaneously is great.
I like that the audio is directed towards you so no need to redirect with your hand. However as a result, the sound might be imbalanced, with the bottom (more dominant) speaker overpowering the top/ear speakers unless you compensate in accessibility settings (not worth adjusting imo).
I occasionally remove the case at home when depleted to allow faster charging by itself and keep any heat, if any, away from the iPhone. Even then, there's shouldn't be any concern of battery damage from heat generated when charging both the iPhone and case. I notice most of the heat generated from the case is confined to the bottom of the case where the PCB meets the battery (behind the home button).
The only bug I notice is that the case stops charging when you separate the iPhone from the case while plugged in, which you'd have to unplug/plug back in to resume charging the case itself. It does have some weight and a bit imbalanced holding in landscape mode but it's not an issue for me.