Your polygraph operator's admonition "Don't try to help me" was intended to discourage polygraph countermeasures. His final question, "Did you Google 'polygraph' this morning?" also indicates that he suspected you may have used polygraph countermeasures.

Polygraph operators are concerned about polygraph countermeasures such as those documented in Chapter 4 of The Lie Behind the Lie Detector because they are effective and they don't have any proven means of detecting them.

However, the mildness of your post-test interrogation (the absence of any direct accusation that you lied or used countermeasures) suggests that you probably passed or that the outcome was at worst "inconclusive."

The fact that the agency with which you're applying is continuing looking into your background after receiving your polygraph results is further indication that you did not "fail."

As for signing any paperwork at the end, I expect that such practice depends on the policies of the agency involved.

You're very welcome. I hope you receive good news soon.