Unlock the Skillbook for his 30% tai dmg, if upgraded it will last for the whole 10 rounds and it won't be cleansed by Han / masked man.

Nope, auras would cease to exist if the "caster" is defeated by the opponent and come back if the ninja is reanimated.

Tobi and hashi's passives, after breakthrough, are casted at the beginning of the match like usual. The only difference is that they aren't dispersed by cleanse. I can't really say if those skills are lost on the death of the "buffed" (not the "caster") or are still present even after the reanimation, since i've never tested it myself nor read about it.