Then there might be the root cause of all your problems. Your hostname should be a FDQN hostname and never a domain name.
So change your hostname to server.domain.com and have your domain just domain.com then it should be fine.
Hello there
server hostname
server.xxxxx.com
I corrected it. Is it normal to see "Local Data" (no) in DNS records? Shouldn't it be YES? If YES is required, where can I get YES?
As seen in the picture
With the hostname, so server.domain.com it is normal dat local data is NO and local mail is YES.
So it's correct as shown in this last image, no need to worry.