as noted, and just reiterated for clarity, it is only with th eintroduction of Final Cut Studio 5.1 that the license has changed to allow this. if you are using an earlier version you are not permitted to do so.
download Perian https://www.perian.org that is a very useful quicktime component bundle for non “Mac” standards.
failing that, on your PC download and install VirtualDub https://virtualdub.sourceforge.net/ then open the errant AVI and use File > Show File Information (or some such) … that should show you what codec et al is involved
wel then “Repair” mu friend. press the “Repair Permissions” button … or are you in fact talking about “Verify Disk” (the button the right) not Verify Permisions?
audio ducking is not in FCP’s feature set at present … if you feel this would be an valuable function for you, then head on over to the feedback page and submit it as a feature request. you can directly access the feedback page from within FCP by going to the Final Cut Pro menu > Provide Feedback
you said you ran “Verify Permissions” and it came up with an error …. are you sure that Apple didn’t tell you to “Repair Permissions”? that would be the normal advice.
Media Manager is a powerful tool which can be dangerous to your sanity if used improperly … i would suggest you investigate only the “Copy” option, don’t even think about playing with any of the other options yet.