Any time an application crashes, it's good practice to clear your preference files since those files get updated continually.
When you launch Final Cut after hearing clearing preferences, it should open to a fresh, empty library. If you then navigate to the personal library and it crashes the application, you can be pretty certain that the library is corrupted. At that point, I'd once again clear the FCP preferences an then close. In the Finder, navigate to your Final Cut Backups folder (usually in Movies) and double click the library that's the most recent prior to the start of your permissions problems.
If opening/updating the library backup also crashes Final Cut, shut down the system and restart in Safe Mode. After it completes the log-in process, restart and (once again) clear FCP prefs. Restart your computer and try again.
If none of this works, you could attempt to rebuild your user account – or use the new one as a dedicated editing account (with Fast User Switching enabled it wouldn't be too inconvenient). Sorting out user accounts is tedious and probably should be done by someone who's successfully done it before. It's entirely up to you, but if it came to this I'd either use the new account for video, or I'd do a clean install of the OS. (Naturally, you'll want to have a complete backup and critical settings documented before you do that.)
Russ