I haven't investigated this recently, but last time I did, I posted this reply:

That site (live.mozillamessaging.com) is used for the little welcome message that appears below your Inbox when you first start Thunderbird. If you click a message, its content should replace the welcome message. No?

Certificate errors in Thunderbird can be caused by a range of issues, similar to those affecting Firefox. These include security software that filters your browser connections (e.g., Avast, BitDefender, ESET, Kaspersky), parental control software like Microsoft Family Safety (to test by turning it off, see: http://windows.microsoft.com/en-us/wi.../turn-off-microsoft-family-settings), and/or malware.

(Malware was the issue in: live.mozillamessaging.com uses an invalid security certificate. The certificate is not trusted because no issuer chain was provided.)

If you use any of those security programs, Thunderbird probably can be set up to work with their filtering, which also may help avoid missing content in HTML-format messages. Do any of them ring a bell?

Dear Jscher, thank You for reply, unfortunately it did not help. On my Laptop, i am not able to receive EMAILS. On my tablet, i am!!!! The error message is gone by clicking an email, but furtheron in am not able to receive new emails. I don't have family settings activated, but I am using Avast. Can you help? THANK YOU!,

I think Avast has a feature called Mail Shield that affects checking for mail, and Web Shield that affects showing web content. You might need to adjust both of those.

Could you try these articles:

• Avast FAQ | Avast 2015: Warnings about invalid mail server certificates when sending and receiving e-mails
• Actually, I didn't find the article for Web Shield, but I think the approach to importing it into Thunderbird would be exactly the same after exporting the avast! certificate for Web Shield.