Everything works fine now!
Here is an update that I hope will help others who are moving from iPhone to Android. I found a great, simple, FREE app that syncs all the music in iTunes to Android quickly and easily. It's called Easy Phone Tunes. You have to download it to your PC or Mac, and then on your HTC device. Plug in the One with a USB cable and press "synchronize" and ALL my music was transferred, including all purchased songs.
I also managed to connect my HTC One with my car's Bluetooth. I restarted the phone and tried to connect again, and it worked.
So all is good. Thanks for the help and advice.