Hello everyone, after a while we managed to solve our issue. Our main issue was the HELO. No matter what host we picked, it always said HELO error. So I found a workaround and now the system is working flawlessly.
What I did is, got inside the OSticket folder, got into the Include folder and then into the Pear folder. Then went inside the Mail folfer. There I found a file called SMTP.php. I edit the file, to be more specific, the line 134
That is what the file said by default. I changed the string from localhost to ācomputername.domainname.comā (The FQDN) and now it just works.
Thank everyone for your help! Hope this helps someone else too!