EricJH, thank you for your reply.
1. It is not baloon messages that are the problem. I have automatic updates turned off and update AV definitions and CIS manually when CIS tells me to. So I'm not being bugged by any balloons.
It's the COMODO Internet Security main program window that pops up in the wrong place of the dual monitor desktop when opened via double-clicking the tray icon.
To picture it better, please take a look at the following screenshot:
After the CIS window is moved to primary display desktop area, it remembers its position for the current Windows session. It resets after the computer is rebooted though.
2. Thanks, I'll try this ASAP.