This "Received" section describes the path of your letter from webmail to plesk mailserver (postfix). i.e.:
your postfix mailserver received this letter from your webmail.
So, why do you think Plesk mailserver helo does not work properly?
Check "Received" on plesk->gmail stage. there you should...
Hm... than that's serious mistake in french locale. It definitely should be reported to Plesk team.
Originally, plesk mailserver screen have no option to manage SMTP banner, but you can manage there SMTP greeting which plesk mailserver will use as a HELO with connection to destination server.
No.
You are talking of two different things.
It's Server SMTP Banner and it has nothing to deal with how Plesk configured to send outgoing mails.
Do not mix SMTP greeting and SMTP banner.
Well, now you have mixed up packages I suppose.
Some of plesk packages are still for debian 6 system and you should manually upgrade them to debian 7.
The problem which you have to solve is to compare packages on your system with clean install plesk for debian 7 and upgrade yours with force...
Check you have Nginx enabled in Plesk panel -> Tools&Settings -> Services Management
Enable it in Plesk
nginx will not start by # service nginx start if it's disabled in Plesk
hm... it definitely should contain selinux logs in case you have audit daemon disabled.
Try to temporary disable Selinux and restart services like mariadb, nginx, psa... to finally exclude Selinux from list of possible reasons.