Star Fragments

Do these stack? If so, how do they stack? Is there a maximum value for their stack?
a) Does obtaining multiple Star Fragments stack the bonus and then they’re all used up?
b) Does obtaining multiple Star Fragments keep a counter that gets decremented on each loot collect?

Do the Star Fragments influence any of the following:
a) Breakables
b) Duty Rewards
c) Artifact Event (swords in the Life realm)

Do the Star Fragments still enhance loot gain after attaining maximum Loot Hoarding or Duty Rewards (if they function on that)?
Does it stack with Diabolic Intruder?

Do the Star Fragments persist if you return to the castle and/or enter a new realm?

Yes, and they stack with similar effects. They’re used up all at once whenever you receive -random- loot from a chest, a duty reward, etc. Therefore, they are not used for breakables, finding artifacts in realms, or anything like that. And no, they do not persist between realms.

Do they help with rewards from defeating monsters? Or just chests and duty?

It helps anything that involves you receiving random items. You don’t typically receive items from battles (not that I can remember, at least) so it won’t do anything for battles.