More info:
used my old HDD with a previous Win7 x64 installation in my current PC for testing. Old Avast, old FF. Here are the results:
FF 27.0, updated Avast: no file downloading in FF with shields ON possible, no disappearing add-on problems.
Updated FF, previously updated Avast: again no problems with net access or FF add-ons.
I have started updating the OS to see if any OS update might be the cause of this conflict.
Regards,
Karel