To answer your first question: There's so much I don't know about Mac OS and I wasn't sure if my Time Machine backup would back up my iMac mail folders. Also, I have low confidence when navigating backup restores and using Time Machine and I know my iMac is getting old and things are starting to fail so I've been gradually removing data to other devices or storage. I don't really know what I'm doing so I have to be careful.
I didn't know about transferring between two Macs!! Thank you for that! I'm still learning. I would try that if I could see the screen. I hear the machine running with the black screen and am hoping it's only the screen and that it is still booting up, albeit dark.
I so appreciate all the expert advice I get from his site.