Hello Frds,

For On-premises Exchange Server with (Outlook Anywhere enabled with Self Signed Certificate) and NOT with SSL certificate: -  Can we access OWA from Internet? Using http?

Yes you can. Ensure no redirect configured in IIS.
and access owa by typing http://mail.domain.com/owa

Thank you MAS...

Another question, Can we access Outlook in same scenario using:

1. IMAP

2. POP

3. Outlook Anywhere

???

Outlook anywhere will not work without certificate installed in local PC certificate store.

I suggest you buy cheap certificate for $30-40 from namecheap/startssl or any certificate of your budget and get rid of this headache.