Do you have the base trim Mazda3 sedan? CarPlay wasn’t available on the base trim on the Mazda3 sedan.

What happens when you connect the iPhone to the USB cable? Does it charge? Is the iPhone available as an Entertainment source?

Do you have Siri enabled on your phone? Are you using a licensed Made For iPhone cable? If Siri is disabled, CarPlay is unavailable and if you’re not using a licensed cable, there’s a chance it could only support charging and not data.

Is the USB flash drive FAT32 formatted? The system will only recognize FAT32 formatted USB flash drives. If you’re using a Mac, it doesn’t use FAT32 as a default, so you’ll have to specify FAT32 when formatting the flash drive before you load the files onto it.

As far as the phone not playing music when connected via USB, does the phone have music stored locally or is the content being streamed? If there’s no music saved to the phone, the system won’t recognize any playable content.

You could, but very few people would do that intentionally. Any reason why you’re considering doing this?