Is there a log of POPcon's actions — where can I find it?

Yes. POPcon logs all activity to a text file:

C:\Program Files (x86)\POPcon\POPconSrv.log

Open it with any text editor (Notepad, etc.). The log shows every mail retrieval cycle, each message downloaded, delivery status, and any errors.

Log file size and rotation settings are configured on the General tab of the POPcon configuration.