It's not meant to be mechanically difficult for players to do, so...
I would say that during any "downtime" (that is, not literally in the middle of combat), players can alter any one of Hazou's aspects that is not his High Concept or Trouble as part of a standard Plan vote. Must include a brief explanation as to why the Aspect has changed and what the new Aspect means; may be subject to GM veto if it somehow seems unreasonable. For instance, he recent reunion for his mother could easily justify some kind of, "Do it for Mom" aspect if players thought that was now more important than one of his other aspects.
Altering an Aspect of an NPC may be possible in some cases, but it's hard to put any concrete rules to it because every one will be different. I don't know how long it will take Yukino to convince Zabuza to give up "Forever Alone" or if it's possible. Probably such things should just be left to GM judgement. Happily, it's not a decision with a lot of mechanical consequences if you screw it up, so no big deal.
Aspects are generally long-term things though, so giving the players basically free reign to juggle Hazou's aspects around as we please doesn't really fit. A flat rate of permission to change aspects would let us do stuff like swap out cleverness aspects for combat aspects as we prepare a fight under the justification that Hazou probably feels upset/confrontational/prepared to fight, etc.
At the same time, the things that make up a person's aspects sound like the sorts of things that can change in the middle of combat. For instance, if Noburi dies in a fight and we're planning the rest of the fight, it could be justifiable for Hazou to, mid-battle, drop an aspect to pick up a vengeance related one. A single codified rate may introduce irregularities on
both ends of the spectrum.
Since aspects directly relate to characterization, that puts them at least somewhat out of character-building territory like XP expenditures, and more into narrative character-building that the QMs control. At the very least, I expect a major event would allow the QMs to impose an aspect on us, and similarly for repeated moderate events.
Apart from imposed changes, though, I imagine an aspect, barring a really major event, would last for at least one arc, so to speak. If we gave Hazou an aspect just before stumbling upon Hidden Mountain, we shouldn't be able to remove it until after we're gone, and even then only if Hazou's meaningfully changed over that time period.
I'm not sure what to think on handling it inside action plans or outside of them, be it in separate votes or just dialogue with the QMs, but I do think that instead of a general 'you can change an aspect this often' rule we should have a 'your aspect lasts at least this long, and longer if you don't change' kind of rule.