Also don't forget the tests you add help you with the regression tests. The large set of tests would assure you that the new fix you do will not lead to any other bugs that
you had fixed earlier.
It is, but as bug crop up you can add tests to ensure they don't crop up again. While it's not possible to ensure perfection, it does help ensure you don't 'revert back' to past problems.
Perhaps not, but you can supply test cases for known problems you might encounter, as well as ones you've solved after they've been encountered.