Its actually pretty good on noise cancellation. Everybody tells me I sound pretty clear & loud. The volume is pretty good. I've never tested it with the windows down but its pretty loud in my opinion.
My phone is in an Otter box and I’ve never had a problem doing whatever I needed to on my phone. The Otter Box hasn’t hindered me in anyway regardless of the app I’m using. Btw it has saved my phone from getting busted up more than once.
While not specifically showing the Moto G5 Plus, the Jabra pairing guide shows G5 and G5S, so the Jabra Classic may work with your phone. Their guide is at this webpage: www.jabra.com/support-page/bluetooth-pairing-guide.
That is very odd, I use this device every day with my Samsung Galaxy 5 (android phone). Be sure to download 2 files from the Google Play Store, and they will help you connect the device.