Are you using the Unified folders view?

Yes. Attached you can see my unified folder view with 5 different accounts. Way below, you can see the Archives folders, one of which is labelled 1 UPF. The emails I am trying to delete are in this folder.

What you're experiencing is a result of how Gmail stores and manages messages. Gmail doesn't use real folders, instead it uses "labels". What you think are folders (they look like folders) are actually labels. The Archive folder in Thunderbird actually points to the All Mail IMAP folder in the server, which is the only true folder in Gmail. As the name suggests, ALL messages in your Gmail mailbox are stored in that one true folder. Find more info here Thunderbird and Gmail then check what you've configured Tbird to do when you delete messages in that account.

Go to Account Settings > Server Settings for the affected account to see what Tbird does to deleted messages. You should have it configured to move deleted messages to that account's Deleted/Trash/Bin IMAP folder, although Google advices against this because they get permanently deleted when the Trash folder gets emptied utomatically in 30 days or when you manually empty it. Also, messages moved to the Trash folder do not appear under the All Mail folder, so this should work to get rid of them.

There is no point in checking for new messages in the All Mail folder when getting new messages for that account. That option should be disabled, because the messages in the inbox are actually already present in the All Mail folder. Right-click the 1 UPF archive folder > Properties then uncheck that option if it is checked. This should stop new messages from getting "received twice".

Thanks, Stan.

I just want to make sure I made the right corrections - please see attachments.

First, I changed the server settings so that when I delete a message it is removed immediately. I previously had it as "mark it as deleted."

Second, I deselected "include this folder in Global Search results."

Did I get it right?

Many thanks,

Francisco

First, I changed the server settings so that when I delete a message it is removed immediately. I previously had it as "mark it as deleted."

That won't do anything different from "marking it as deleted" for Gmail. The message will still appear in All Mail and the Inbox when you restart Thunderbird. Use the option to move it to a folder, then select that account's Trash|Deleted|Bin folder, whichever name is used on your Gmail account. This will remove them from Inbox and All Mail, but they will remain in the Trash folder until they are removed from there as well. You can configure Tbird to empty the Deleted folder upon exit, but I wouldn't advice doing so if this account is used for important communications. I recommend manually removing stuff from the Trash only AFTER reviewing them and making sure nothing important is in there. Taking that approach at least gives you a reasonable time window to recover accidentally deleted important messages. You may not think much about it now, but when it happens, you will appreciate having that leeway.

Second, I deselected "include this folder in Global Search results." Did I get it right?

Nope. Re-enable that option. It is the second option immediately below it that you should disable, so that the archive (All Mail) folder is NOT included in the checking of new messages.

I did as suggested.

Many thanks, Stan.

Francisco

You're welcome.