Can I make cds, for personal use only, from Amazon Music through Audacity,or would this be illegal?
Yes, it’s illegal and a violation of your streaming agreement. There’s a reason why they don’t give you a “download” button. 
The artist (or copyright holder) gets paid a fraction of a penny every time the song is streamed, or a few cents if you buy a download.
Amazon Music is also a music store where you can buy and download individual tracks or whole albums as MP3 files (I’ve bought a few albums from Amazon Music in the past), and you can legally burn those MP3 files to a CD for personal use if you want to.
But Audacity doesn’t handle CD burning; you’ll need a separate application for that.
I believe iTunes still sells downloads too. They are AAC (MP4 or M4A) rather than MP3.
Yeah, I was a little surprised that Amazon is selling MP3s rather than AACs. It could be a licensing issue for Amazon (AAC requires a license while MP3 does not anymore), or it could be a compatibility issue, so that people can still use their music players from the '90s. 
IIRC they’re 320 kbps, so they’re close enough to transparent to me (I actually bought them for my son, and he hasn’t complained about the quality).