This is because IMAP always keeps all messages on the server until deleted. The messages on your PC are just copies, but the 'real' message is online. This allows you to have full access to mail from multiple PCs or phone.

So if I delete a message from one device it is gone, and cannot be downloaded to another device? It surely did not work that way with POP3 and seems like taking a step backwards.

That is because POP lets you download to PC and leave on server. It depends on what you want. Many like IMAP because it creates a consistent presentation of your messages so they can be viewed and responded to from any device. And you can see the sent messages from anywhere. There are more people switching from POP to IMAP than the other way around. Still, it's a matter of preference.

I read online that in setting up Thunderbird one had the option of declaring to leave a copy of the message on the server and for how many days. Was that just for POP3? (Yahoo requires IMAP)

I cannot believe there is no way to use Thunderbird on Win 10 desktop, and then IOS Mail Yahoo on iPad and one app not know of the other's existence.

Do you know of any 2 apps that can coexist that way?

Those features are just for POP. I don't know why you would want to delete a message on one computer, yet keep it on another. I encourage you to give IMAP a try, as it provides a consistent view from all devices. There are only two options for email: POP and IMAP.

Thank You for putting up with me. I will do as you suggest.

On another note- with IMAP- can Thunderbird be configured to only download new messages when I ask for them? I think that would help me to know when (just for me) to delete certain messages.

No, IMAP is always alive, since it is viewing directly to the server.