Didn't solved the problem for me with my BFD3 standalone 64/32 bit under OSX 10.7.5. App is constantly crashing (opening, showing alert windows about "Restore Windows" and/or missing licences, three seconds later -> crash with nearly the same crash report as posted from the original poster here. Had uninstalled/reinstalled the complete BFD3 software (incl. re-downloading it) several times with no effort.
Luckily i could manage to license it through the AU plugin in Live9, all is working good there.
Attached is the latest BFD3 Runtime.log after a crash
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All your permissions look correct... From the log it looks like none of the PNG resources are being loaded... Wonder if it's because you're running OSX in German.. Your best bet is to wait for a response from the FXPansion crew on this ( I take it you created a support ticket).