After talking to mjacob, I now understand why the pypy-c tests were failing so badly.
Re the pypy/python2 errors: It looks like there might be some bug in pytest. If you try running this command:
pypy pytest.py pypy/module/_hashlib/ pypy/module/faulthandler/
It should fail with the same error seen in the python2 pastebin above.
I now understand that the buildbot must not run these two tests in the same test execution, explaining why the behavior I'm seeing is different.
Given all this, I think I now understand this correctly. Thanks again to mjacob for explaining!