1) I have a lvl 2 Criochant and lvl 1 Disowned both equipped with a Taproot Blade. First Taproot Blade destroys a curse for its bonus and the second destroys the hero that carries it...but I have Bracers of defense that when a hero it to be destroyed or discarded to discard that card instead.
Does this work?
Seems reasonable to me. You use the Blade's power to destroy the wielder, but the Bracers' power keeps the wielder alive and still carrying said blade instead of dropping to the floor dead (and dropping the Blade).
2) Similar scenario with a lvl1 Disowned, but facing a creature with the Edgewalker's Blade (Battle: discard 2 heroes) since I have only 1 hero and am protecting it with the bracers, is it protected until the end of turn by the effect or is it discarded by the second of 2 heroes to be discarded, since I have only one?
It's one effect, so IMO you resolve the entire effect first, run into the "Do what you can" rule where you only attempt to discard your one hero, and then the Bracers save the hero after you resolve the Battle effect. Or, to put it another way, if you didn't have the Bracers, you wouldn't try to discard your hero twice, so you shouldn't have to try to do so because you have the Bracers.