[She knows about devil's proofs, and honestly she can't help but sigh at how flimsy this argument is.]

Then perhaps they could be checking for that. Although I honestly think it's not smart to bring rope with them to a trial. And just because I can't prove either way doesn't necessarily mean it's relevant to this particular case. The mastermind probably knows more about the particulars, but she won't be able to answer you right now.

[For obvious reasons.] The mirror doesn't appear in Tamamo-no-Mae's myth. However, the name of it seems to be based off of the goddess of the sun and universe, Amaterasu. Which means that it might be the sacred mirror, the Yata no Kagami. The mirror itself was forged by Ishikoridome in order to lure out Amaterasu.

The myths never spoke of the mirror having any special properties, however.