Hi. I had hassle setting my email to work with Avast. Your screen shot of Avast Mail Shield shows Port 110 for POP3 and no send protocol at all. Are you sure your email provider doesn't require SSL? (Windows Live Mail sucked for me by setting what it thought should be my email ports and that in turn confused Avast).
The knack is to have only non-SSL ports in your email software, and then make sure the SSL ports show up inside Avast's Mail Shield.
Also make sure your username in each account is the full email address.
Even if your email provider requires SSL, don't set SSL in your email software. Instead set non-SSL ports:
Port 110 for POP3 (send)
Port 25 for SMTP (receive) or
Port 143 for IMAP (receive)
Send test emails from/to each of your accounts.
Then open Avast > Realtime Shields > Mail Shield > Expert settings > SSL Accounts.
Make sure each of your email accounts show up twice, once for POP3 (or IMAP) and once for SMTP. Avast should have added SSL encryption, protocol and SSL port for each account:-
Port 995 for POP3
Port 465 for SMTP or
Port 993 for IMAP
See my example screen shot for two accounts...
Amend the entries by hand if need be. Though I've found this to be non-sticky.
Worked for me.