Hello everyone,
My problem resolves by this solution:
Getting Hostgator (preferably) or other external Domains Mail Server to work with Odoo community 13 on Gcloud.

Setting up Outgoing SMTP: 
(SSL None)

Server name: mail.mydomain.com (on Hostgator)
Port 26 (25 won't work it connect only to 26)
Email: catchall@mydomaine.com (domaine provided by hostgator)
Pass:********

Incoming IMAP:
Server name: mail.mydomain.com (on Hostgator)
(SSL None)
Port 143
Email: catchall@mydomaine.com
Pass:********

Message shows: everything working fine, same for confirming connection in incoming mail.

Problem: sent messages/quotation/bill to external emails declares no error as everything is working, but nothing sent nor fetched from my Hostgator Email Server.

I give a check on my log file and found this:

_odoo odoo.addons.mail.models.mail_mail: Mail with ID 121 and Message-Id '<(My ID of message i guess)@(here my company-name (unrelated to Email domaine name))>' successfully sent 

2020-10-17 14:28:56,826 1745 INFO bitnami_odoo odoo.addons.mail.models.mail_mail: Sent batch 1 emails via mail server ID #False 

Note1: Alias domaine empy in General config

Note2:  Email works fine (send/recieve) on other clients like Outlook and Server test (https://www.dotcom-tools.com/) SMPT POP IMAP are all working.

Note3: ''catchall'' as a email was just a desprate attempt to make this works based on a a solution (that didn't work) to name records.......  

Note4: Am open to alternatives (if there is any) that may give me a working email system with the @mydomaine.com of my company of course.

Update Note1: Just found out that if i send an Email from odoo using cachall@mydomain.com to an email receiver inside the same Hostgator Mail Server like random@mydomain.com (for exemple) then catchall@mydomain.com recieve the Email successfully, now the problem revolve around how to make Odoo use my server to send emails to external users from my Email Server (@gmail.com; @exemple.xxx .....)