No, you wouldn't be able to interchange displays between generations of iPhones. The 8 uses a 3 channel, temperature sensitive light sensor. The 7 uses a single channel, light only sensitive sensor. The ribbon cables are also likely different.
*Get another AirPods case and charge YOUR AirPods units in another case to determine if your case, or either AirPod is bad.* Do you have any friends that have AirPods? If so ask them if you can put your left and right unit in their case. If both of them charge you'll know they are not the problem. The problem likely lies within the charging case. You can buy another case from Apple for around $70. If your AirPods don't charge in another case then the problem likely lies with the AirPods. If they do charge I suspect your charging case is to blame.
I've found that keeping the AirPods case in the "coin pocket" of my jeans helps with any damage. Some jeans they may fall out of that pocket. So I recommend trying this at home for a few hours before leaving. I know this doesn't help with damage you already have, but will with preventing future damage.
Blown engine... Okay, I know the sound you're talking about. I tried everything! I plugged in the lightening connecter. Plugged in headphones. Nothing helped this awful sound. It got a lot worse as time passed. When I 3D touched an app that didn't support it and the Taptic Engine made the 3 short taps, I never got the sound. By the time of writing this, the iPhone 6s Plus was doing it even then. What I heard was a buzz, that while constant did have some come and go as far as loudness. It didn't start this way, but it was acquired with time. Over the course of having the phone for a little over a week. All down hill. The sound only happened while the phone was laying down, screen facing up. My best words would be to really put your Taptic Engine to the test before you decide your new iPhone 6s Plus is for you. Create a custom vibration tone for one of your contacts. Really lay on it. Have no mercy. I feel like if it's going to break, it will be during this time. Replay a few times, over a few days. You have...