Let's consider the concept of Citizen's arrest. Wisconsin law is not silent on the matter, although there is no statute on it - e.g.,
State v. Slawek, 338 NW 2d 120 - Wis: Court of Appeals (1983),
citing Keenan v. State, 8 Wis. 132 (1858) ("Any private person may prevent the commission of a felony, upon the same ground that an officer may prevent it.").
So for the sake of brevity, my understanding of your post is that Wisconsin case law suggests that that a citizen's arrest in the prevention of a probable commission of a felony is lawful, as is a citizen's arrest for a misdemeanor if a breach of the peace requires it for public safety against acts that threaten or incite violence.
After skimming your cases I found notations that in certain situations, in particular when a citizen witnesses a criminal activity by a person (e.g. that person robbing a house) he may make an arrest. I found nothing to suggest that a citizen has either immunity from his/her making mistakes, or that just a "probable cause" (or in this case "speculative cause"...such as hearing gunfire from somewhere) is sufficient. Nor have I noted a duty of an innocent citizen to allow such an arrest, or a surrender of his/her rights of self-defense from a mob chasing him/her.
To be specific: this is not a question over the lawful or unlawful intent of those chasing him, or over if they had "probable cause". Whether Rosenbaum was just intending to use deadly force, or just yell is irrelevant. Whether Grosskreutz or other assailants were attempting murder or just a citizen’s arrest is irrelevant to the lawfulness in use of defensive force. Intentions don't matter.
And on that what Wisconsin use-of-force law requires in the context of self-defense is pretty clear.
Wisconsin §939.48. explains self-defense and defense of others, and it privileges the use of defensive force against an actual threat of harm, but also the use of defensive force against what the defender “reasonably believes” to be a threat of imminent serious bodily harm or death to him/herself.
Look to Wisconsin jury instructions on this point,
Wisconsin Jury Instruction Criminal (WJIC) 805. Privilege: Self-Defense: Force Intended or Likely to Cause Death or Great Bodily harm. It addresses §939.48, but also adds:
"A belief may be reasonable even though mistaken."
Therefore, it does not matter if those shot were actually engaged in unlawful acts of imminent deadly force aggression, but rather whether Rittenhouse’s perception of them as being engaged in unlawful acts of imminent deadly force aggression was a reasonable perception.... which, obviously, it was.
