1. Did this message come from Tbird or Hotmail? If it was from Tbird, what is the size (mb) allowed in the Tbird inbox?

Most likely from Thunderbird.

2. Is there a way to prevent the large attachments from being downloaded.

At the top right of the Thunderbird window, click the menu button > Options > Account Settings. For an IMAP account: Select Synchronization & Storage for your account in the left pane - Disc Space. Check the box 'Don't download messages larger than' and set a value for the size of the message.

For a POP account: Select Disk Space for your account in the left pane. Check the box 'do not download messages larger than' and set a value for the size of the message.

3. Why would I have received the message about the 1,000+ emails in my Inbox?

It's possible your Inbox mail file got corrupted. Try to rebuild the index file of the troubled folder. Right-click the folder - Properties - Repair Folder

Note: depending on the corruption this may erase messages from the affected folder which cannot be recovered anymore. In that case you'd need to restore them from a recent backup.

Corruption is often caused by anti-virus software messing with Thunderbird mail files. It is therefore recommended to create an exception for the Thunderbird profile folder, so that the real-time scanner won't attempt to scan the profile folder with your mail.

For more information on the profile location see http://kb.mozillazine.org/Profile_folder_-_Thunderbird

Also see http://kb.mozillazine.org/Disappearing_mail

I did some more investigation of this problem and found that one of my yahoo accounts that I rarely use had 197 emails, all the same email, the one shown in the screen print. I think I screwed up because they were taking up 8gb and I deleted them. The one shown came in after I deleted the 197. Unfortunately, I also deleted the original off the Yahoo server so this problem with this particular email probably won't happen again. However, this is not the first time this has happened, also on a yahoo account. So when it happens again I will contact you sooner and I won't be so quick to clean up the crime scene.  :-) I will also do a folder repair on this account and maybe that will prevent it from occurring again. If you have any other suggestions rather than the folder repair, please let me know. Thanks.

Okay, here's the latest on this problem. I thought I'd deleted the email off the Yahoo server but I lost internet connection while I was doing it and evidently, the delete didn't happen. So now the problem is still occurring. As you can see in this screen shot, there are now 3 copies of this same email. What can I do to correct this? Do you want me to run the Folder Repair and see if that stops it? I'll wait to hear before doing anything. Thanks for your help.

Login to your Yahoo account via webmail and delete the offending message from the server. Then delete any local copies in Thunderbird. Do the 'Repair Folder' for Inbox. Compact folders. http://kb.mozillazine.org/Compacting_folders

I took your suggestion and deleted the email on the yahoo server, deleted the copies in Tbird, and did the Repair Folder. However, I have concerns about doing the Compact Folders. The last time I did that, over a year ago, I thought only the folders in that particular email account would have the folders compacted. When I ran the Compact option, I lost a lot of emails that I should not have. They seemed to still be on the server but not available in Tbird. I tried everything I could think of, including Syncing and nothing would get them to appear in Tbird. So if I have to log in to the server to get the info I need, then why use Tbird? And that is why I haven't Compacted my folders since then. It tells me that I would save 7gb so I have to weigh that against the aggravation of logging into the email server every time I need info from a particular email. Is there a way to get these missing emails to download after doing a compact? As I said the Sync didn't work.

The last time I did that, over a year ago, I thought only the folders in that particular email account would have the folders compacted.

This is exactly how it works.

When I ran the Compact option, I lost a lot of emails that I should not have.

I'm not going to guess what that means. In any case, loosing messages upon compacting indicates that there has been some sort of corruption before, and compacting is fixing this.

I tried everything I could think of, including Syncing and nothing would get them to appear in Tbird.

Again, I'm not going to guess about this. You haven't mentioned yet what's your account type - POP or IMAP?

And that is why I haven't Compacted my folders since then.

Compacting is necessary maintenance and you cannot avoid it. Please read the article about compacting linked above.

It tells me that I would save 7gb

So compacting is needed desperately. If you're worried about loosing messages upon compacting create a full backup of your profile before. In any case, we can stop here if you think you don't need it.

Sorry for not responding sooner. I've been away from home and my computer. Sorry I didn't specify IMAP because I thought all hotmail accounts had to be IMAP. Yes, I am worried about losing emails by compacting since it happened before. How do I create a backup of my profile? I looked through the tabs and didn't see an option to do that but I might have missed it.

Generally, back up is external to Thunderbird. Fundamentally you make a copy of your profile using your file manager e.g. Windows Explorer.

https://support.mozilla.org/en-US/kb/profiles-tb?esab=a&s=profiles&r=1&as=s

Windows users can use MozBackup to simplify matters.

http://mozbackup.jasnapaka.com/

This add-on:

https://addons.mozilla.org/en-GB/thunderbird/addon/importexporttools/

has an option to make backups from inside Thunderbird, but I haven't used it to do this myself.