For the notifications while driving and listening.. I recall at some point while tinkering with an older, rooted, android phone - I could set my phone to automatically turn those notifications off, specifically when I was connected to something via bluetooth. Once disconnected from bluetooth the phone switched notifications back on. I used some kind of app akin to If This Then That, but it's name eludes me now. I guess fucking with an iPhone is far less appealing to achieve something similar! Not sure why I don't have that setup on my current phone and car. Probably laziness.
Yeah. The iPhone OS has a similar function called "profiles", that you can configure for this purpose. But you need to set it up, and remember to turn it on - and off! - and do so BEFORE you get in your car and head out. I just don't sit on the couch watching TV thinking, "oh geez, I should configure my iPhone Profile for driving so my podcast doesn't get interrupted when I go driving on Thursday...." I'm just being grumpy/lazy. Ignore me.
iOS and Android both handle this most elegantly through Carplay/Android Auto. It's possible to run Android Auto on an android not connected to a car stereo. It's not possible to run Carplay. Android Auto basically turns your phone into Android Auto and mirrors it to the car's display, while Carplay is an auxiliary screen for iOS. In each case the different apps in the car stereo modes allow you to set whatever level of annoyance you want to deal with. Doesn't help you with your boom box, I know. Frankly it's all been downhill since this guy.