As for Perrin and Galad, I personally think that Galad will be pretty lenient after what Perrin did at the last battle. Then again, these are the Whitecloaks we're talking about...
I'm fairly sure that is wasn't Laman's sword that Rand gave Tam. I think that Rand actually went into the Last Battle with Laman's sword, along with Callandor, because he mentioned how long it had been since he had actually carried a real sword with him. Also, since Tam fought in the Aiel Wars...