I Installed succesfully mailinabox 0.19a on my Ubuntu Server 14.04.5 (clean install).
I forward ports on my mikrotik correctly - 25,22,53 tcp, 53 udp, 443, 80, 587, 993, 995, 4190 and i check it with paping, evertything is good with forward and ports are open.
I can send and receive mail from and to mailinabox and gmail (not spam) but I still get warnings in status check page:
SSH Login (ssh) is running but is not publicly accessible at
Public DNS (nsd4) is not running (port 53).
Incoming Mail (SMTP/postfix) is running but is not publicly accessible at
Outgoing Mail (SMTP 587/postfix) is running but is not publicly accessible at
IMAPS (dovecot) is running but is not publicly accessible at
Mail Filters (Sieve/dovecot) is running but is not publicly accessible at
HTTP Web (nginx) is running but is not publicly accessible at
HTTPS Web (nginx) is running but is not publicly accessible at
It has to do with running your box behind a router. I had been running my server for almost a year with the same errors you have until I had this reply on my thread.
Btw. If you are hosting your server yourself on a private network you don’t have to have ssh access. I have a vpn that connects to the network I’m hosting my server on so I disabled public ssh access for added security, I just ignore the ssh error on the status checks page.