NethServer as a Primary mail Server

This may depend on the accounts provider you use–with Local LDAP, which I use, you’d just log in with the username, not the full email address. But since it’s an alias, it’s a single mailbox.

Can I able to send emails using a second email domain that I created using an alias.?

Yes, by default there’s no validation of the outgoing email address.

How I can send email using alias account ? I can’t be able to switch to alias account using SOGo.

Can’t help you with SOGo. With a real mail client, you’d just set the desired “From” address in the account settings.

In the mail settings you can define with which account you want to send the mail, see also my picture.

volker@mydomain.de is an alias for volker@home.mydomain.de

This could also help…

can I use IMAP client for the user@dommain.com email account? if yes then how is it possible?? as I am getting these errors while connecting third-party IMAP email client.

Can I use SSl or TLS secured connection instead if none for the second domain email address??

Certainly you can. But if you’re trying to connect to that domain name, it will need to be added to your server certificate.

How I can add this domain to my existing server certificate?

The easiest way is using Lets Encrypt certificates. By adding the subdomains that are running on your server, you will get a certificate valid for all those subdomains.
You can find the certificate in servermanager under Configuration / Server certificate (old servermanager)
or under System / certificates (new servermanager)

When I request a certificate I got these errors as you can see in the attached picture.
Screenshot%20from%202019-10-22%2010-43-17

Lets encrypt validates DNS records. Did you create DNS records (A or CNAME) for your (sub)domains at your domain registrar?

Yes, I already created a DNS record for my second domain

Also for the sub domain(s)??

yes also for the subdomain

is there any problem if my first domain already have an ssl certificate

but when I tried both domains separately it looks like

If I delete all the files under the /etc/letsencrypt/live/ and request again for let’s encrypt certificate. Will it work or not? or will it destroy the whole server?

Do not delete those files–there’s no reason to do so, and you’ll almost certainly break things.

Sadly, the GUI isn’t very helpful with its error messages. It’s possible the system log would have more information, or almost certain that you’ll find more detail in /var/log/letsencrypt.