OS Upgrade

Maybe you have the wrong file system type for Catalina? It seems that you need to format the disk as APFS (see <https://support.apple.com/guide/disk-utility/file-system-formats-available-in-disk-utility-dsku19ed921c/19.0/mac/10.15>). I think 10.13 allowed MacOS Extended.

I believe so. I haven't tried this, but see <https://www.macobserver.com/tips/how-to/upgrade-mac-apfs-after-high-sierra/>, and this discussion: <https://discussions.apple.com/thread/250038736>.

Macintosh HD should be your internal disk. Make sure you didn't select it as the backup disk in System Preferences > Time Machine.

Come to think of it you shouldn't have been able to select it as a Time Machine backup drive unless you did it from an external boot up drive.