I played around some with Amazon Music, I liked it. I'm finding myself on Google music frequently though, despite the lack of "shuffle library" button.
Unfortunately, I can confirm based on my usage yesterday, that the usb port is not charging my phone, and it is actually losing charge while running Android auto. It could just be my phone, a note 4, is too power hungry for the usb port to charge it. I did read on a Hyundai forum site that a usb y cable, Micro usb to dual usb, and a quick charge usb cigarette adapter, charged the phone. I bought the micro usb y cable yesterday, just waiting for it to come in. I already have an adapter that supposedly is a quick charge, so I'm going to try that first before buying a new one.
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Finally got around to checking battery charging on the Sonata, and you're right. My Nexus 6 doesn't charge from the USB port. I'm interested in seeing the results from your cable experiment. Where did you order yours from?