Perrin promised that bit *after* Morgase announced her judgement. It was a way for him to avoid fighting the Whitecloaks.
This wasn't the Perrin that went into the Two Rivers looking to turn himself in to the Whitecloaks. He had a very clear goal going into this, and that was to avoid bloodshed if possible.
By the time Morgase reached her verdict, Galad understood what had actually happened that night, and he agreed with Morgase. That means he no longer saw Perrin as a dangerous darkfriend, so it would have made no sense for him to fight Perrin over that incident. Note that when Bornhald and Byar first told Galad of Perrin, his attitude was careful skepticism. He erred on the side of his men, but was willing to give Perrin a fair trial. This was not someone who had already made up his mind on the issue.
Jearom was beaten by a farmer with a quarterstaff. Very unlikely that he was killed.
Valda certainly had more experience than Galad, but his mindset led him to underestimate his opponent. It's telling that Valda was awarded the title of Blademaster by judgement, not by dueling another blademaster. Swordsmanship is a complete package, and the right mindset is a big part of that. I would say Galad is objectively a better swordsman than Valda: he didn't win by chance, he read Valda correctly and lured him into a fatal trap.
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