Being new to Thunderbird, I highly recommend browsing the many articles available here https://support.mozilla.org/en-US/products/thunderbird. You will soon be right at home with using Tbird.

1) I haven't figured out where the attachments to my imported messages can be found

If you open an imported message that has attachments, at the bottom of the message (reading) pane you should see a panel showing some info about the attachments contained in the message. On the same panel, you should see a button for saving those attachments to a location of your choice.

2. Tbird keeps track of POP-downloaded messages in a file named popstate.dat inside the Mail > {POP server name} subfolder inside your Tbird profile folder. You don't edit it, but if you want to have a look at what it contains, just open it in a text editor.

You could look at the POP download controls offered by your mail provider to see if you could limit which messages can be (re)downloaded. If no such controls are offered, there isn't much you can do on that end. What you could do, however, is change Account Settings > Server Settings and set Tbird to download headers only, instead of downloading all 4000 messages in full.

Thunderbird does not have an internal mechanism for cleaning out duplicates.

3. I can't think of a surefire way of stopping Tbird's online activities other than taking it offline like you did. When offline, change those account settings accordingly then restart Thunderbird. I prefer restarting Tbird after changing download/sync settings to force a new session that respects them.

Being new to Thunderbird, I highly recommend browsing the many articles available here https://support.mozilla.org/en-US/products/thunderbird. You will soon be right at home with using Tbird.

Thank you. I have already spent many hours searching and reading both articles and community forum posts. I hope it leads to more intelligent questions. I have been thinking in Eudora terms for decades and have some preconceived ideas of how email apps work that don't neatly align with Tbird.

1) I haven't figured out where the attachments to my imported messages can be found

If you open an imported message that has attachments, at the bottom of the message (reading) pane you should see a panel showing some info about the attachments contained in the message. On the same panel, you should see a button for saving those attachments to a location of your choice.

What I see at the bottom of the message pane is the path to the attachment's location in the Eudora subfolder for attachments. I take it that means that the import from Eudora did not move the attachments because they already had a local location. Which in turn means that I should not delete my Eudora data files or I will lose all my attachments, since I have no intention of going through 20+ years of emails to save them individually to a new location. Probably not a big deal since I had no plan to delete Eudora in the first place.

2. Tbird keeps track of POP-downloaded messages in a file named popstate.dat inside the Mail > {POP server name} subfolder inside your Tbird profile folder. You don't edit it, but if you want to have a look at what it contains, just open it in a text editor.

Thanks for the file name. Disappointing that it's not editable, but not unexpected.

You could look at the POP download controls offered by your mail provider to see if you could limit which messages can be (re)downloaded. If no such controls are offered, there isn't much you can do on that end. What you could do, however, is change Account Settings > Server Settings and set Tbird to download headers only, instead of downloading all 4000 messages in full.

Thunderbird does not have an internal mechanism for cleaning out duplicates.

This started me thinking that maybe a better plan would be to regard the POP account as historical and open a new IMAP account. Then I could just download the existing email from the server and the duplication wouldn't matter. However, three questions arose: 1) I don't really understand the concept of mirroring. If I run filters on downloaded mail on my PC to sort messages into folders, will that function mirror on the IMAP server? Do I need to have all the same folders created on the server? Or does mirroring simply apply to downloading, sending, drafting, changing status from unread to read, etc.? 2) In the same vein, if I use the same filters that I created for my POP account, do I need to create all the folders that messages get sorted into in the the local IMAP account? I'm assuming Yes. 3) The reason for this whole exercise is that my ISP is going to stop providing email service itself and migrate everyone's email accounts to Google Mail. (That's their GSuite product, not Gmail.) If I create a new IMAP account with my current ISP's details in the the settings, will I be able to just edit the settings to the new Google imap and smtp server addresses after the migration happens, or will I have to create yet another new account?

3. I can't think of a surefire way of stopping Tbird's online activities other than taking it offline like you did. When offline, change those account settings accordingly then restart Thunderbird. I prefer restarting Tbird after changing download/sync settings to force a new session that respects them.

Odd that there's no Stop button. I realize that not everyone is beginning in the middle like I am with several GB of existing mail, but surely there must be other circumstances that would call for a download (or, indeed, other actions) to be interrupted in a hurry. Just MHO.

Thanks Stans for taking the time to sort out my questions and confusions. I appreciate it.