If parent classes are already tested then avoid duplication and just test the new aspects of the child or any aspects that the child changed.
Not sure - have done very little PHP.
Yes => test all aspects of the method.
You could have some unit tests that test performance but they would be focused on performance where as others may be focused on testing functionality. Don't mix both in the same test.
Ideally you should run them every time and often. Sometimes if the execution time is huge you might want to consider refactoring them into smaller suites and then only executing the effected suites when something changes - but still do everything periodically.