When you run Root of Warrior, Mifune is immune to all debuffs. This means you can no longer apply acupuncture, chaos, or immobile (duh).

However, acupuncture, chaos, and immobile are all debuffs that can keep a mystery from going off( i.e. "interrupting") on top of what they normally do. An example of this is Scarlet Blaze's Imprison mystery. If use against someone with Genjutsu: Mirror Return to stop a mystery, the immobile/imprison is reflected, but you still successfully interrupt the target.

Because of Root of Warrior, Mifune is immune to acupuncture, chaos, and immobile, and his mystery is immune to interruption. That covers just about anything that can stop a mystery. As such, nothing can stop his mystery, save for killing him..

Yes, Immune to Interrupt means just that. When not augmented by RoT or anything else, it's just immune to interrupt and nothing else.

Mifune will ignore Iruka and Gai, but in his default state, can be stopped by any other debuff that debilitates you, like Chaos, Immobile, or Acupuncture.