The fact that the cost does not agree is a bug in the notebook that has been reported, but apparently not fixed yet. Here’s another recent thread about this issue.
But on the back prop tests, if you don’t pass the local tests, it means something is wrong with your code. Notice that the “Expected values” there only show the shapes of things, so getting those correct is a pretty low bar for success. The actual unit tests fail with mismatching values, as you can see in the output you show.