For point nr 4, at our company we tracked how many bugs that were fixed, came back afterwards (project with 80 developers for more than a decade old code base). We saw it's very rare that the same bug (after the fix) will pop up twice, and therefore decided not to add or write regression tests on them, and focus our testing efforts where it mattered more.
It depends on what kind of error it is. If it is an off by one error, there isn't much you can do to test it, but if it is an input edge case you didn't handle correctly, then a test make a lot of sense, if for nothing else to verify the fix.
Of course, it is rare that same bug will pop up twice, but bug demonstrates areas which are not covered by tests, so new test(s) will cover these areas and will catch an other bug(s).
