Problem fixed, Thanks every one… Okay bye!
Woo-hoo, that would be mean, no? 
But more seriously, YES, the problem has been fixed.
The 501 error as nothing to do with the problem. The AUP#EML-005 is “sorta” responsible for my inability to send email.
My service provider decided it would be a good idea (not) to filter on non-mappable addresses [192.168.1.13] when their system decide that someone might be involve in sending and or receiving spam or is outside their AUP…
Here’s the explaination. I recently received an email from MY life insurance advisor that wanted to talk about how to manage retirement plan, etc. (definitely not there yet), and the guy thought it would be nice if he could reach a bunch of people at the same time… yep, 90 in CC!
I wrote him back with the nastiest email you could think of… 
he then sent another message to the same 90 people… mentionning to be careful to not to click on unknown links and they would never ask for personal info in emails, etc, etc. He then wrote me (alone) an email saying he was sorry and people’s privacy was important to him blah, blah, blah… Sure, I believe you!
The consequence of this, I don’t know if it was the amount of people in the emails or my foul language, but the end result was that it was either considered as spam or against their AUP…
Sorry! 
Sooo, what is the fix? With the help of Betterbird’s developper we were, well, he was, in fact able to suggest a preference to add and instead of Betterbird sending and address literal ([192.168.1.13]), which is blocked, send the computers host name for the EHLO argument. This preference was created a long time ago for testing purpose.
See: 4.1.1.1. Extended HELLO (EHLO) or HELLO (HELO)
Instead of sending and receiving this:
mailnews.smtp: C: EHLO [192.168.1.13]
mailnews.smtp: S: 501 EHLO JDBFvggTYD6Em internal error AUP#EML-005
It would send and receive this:
mailnews.smtp: C: EHLO my.host.name
mailnews.smtp: S: 250-smtp.<MY.ISP> hello [xxx.xxx.xxx.xxx], pleased to meet you
I could have also changed my LAN IP address and it would have worked… you can basically send almost(?) anything you want.
The reason is that when you send your EHLO command, and everything is correct, the server recognise you by your WAN IP address and the handshake continues.
The preference you ask? Oh yes here it is:
You can set it in the advanced preference settings in Betterbird/Thunderbird or in a prefs.js file.
You have also 2 choices.
If you have only 1 SMTP server configured (default)
pref: mail.smtpserver.default.hello_argument
string: your.host.name
Or if you have more than 1 server configured
pref:mail.smtpserver.smtpNN.hello_argument
string: your.host.name
NN is the number you get when you look for the SMTP server in
Help -> Troublesooting Information
If you have more than 1, it could be a good idea(?) to also adapt your host name.
By doing this, I was able to send email as I use to.
Now, I will have to wait a few days before I get off of their banned list (I hope) and recontact my service provider just to make sure everything is back to normal. I will probably then remove the mail.smtpserver preference, as I have been told that a fix should land in the trunk enventually. Meaning that instead of sending the address literal it would send the computer’s name (FQDN) by default.
Just in case you’re interested:
Using 127.0.0.1 (nonrouteable IP) as HELO string
And also (the patch):
Attachment #249368: patch v3 -u for bug #244030
NOTE: Look at the dates…
So, that’s it, that is the end of the saga 
Thanks to anyone who tried to help.