IMAP is a protocol that provides access from your email client to mail hosted on an external server like Yahoo, ATT, Gmail, ...
POP3 retrieves email to your email client from an external server
SMTP sends mail from your email client using an SMTP server.
That said, POP3 would not be attemping to send messages, it would be SMTP doing that. As far as POP3 or IMAP, you'll need to decide which one you want to use.
You might find this site helpful: https://help.yahoo.com/kb/SLN4724.html
As far as troubleshooting goes, you can determine what is going on during any of these transactions by reviewing the associated internet session log. These logs are created whenever internet session logging is enabled. That setting is in Tools > Internet Options, at the bottom of the General tab. I strongly suggest reading the associated help information.
Be aware that login credentials are recorded in the logs in a format that is easily decoded. Don't post a log without removing that content. Don't forget to turn the logging off once you are done troubleshooting.
Also, make sure you are running the newest version Pegasus Mail (v4.72).