Based on the help file for Master of Atemi Waza, I'd expect it to boost stuff like backfist, tiger claw and unarmed defense, as well as possibly up melee effectiveness when wielding hands. Is that accurate? Specifically, does it affect backfist and tiger claw?

I believe it boosts the effectiveness/damage of hand to hand fighting in general. Tiger claw probably is unaffected currently, though now that you mention it I can certainly see the case for that. Everything else on your list should see a boost from the edge.

I ask because if that edge only affected melee then I probably wouldn't take it. How often do you fight w/ your bare hands? But if it boosts backfist + tiger claw then I could see a case for taking it just because of those two.

The one about adding half-elves to wood-elf hatred. Wood-elves love it interacial as much as high elves!