It's going to take some analysis to figure out exactly what happened in that sequence of events.

Yes, and I've already spent hours going over the footage, reading the actual relevant Wisconsin criminal codes, etc. I have a pretty darn good picture of what happened that night, as well as to the legality of his actions.

Before addressing the main question of whether he could be convicted of murder/manslaughter, I'll address the side question of whether his possession of the rifle as a 17-year-old was illegal in the state of Wisconsin as some outlets have claimed. 948.60 addresses this question, and put simply, it isn't. The statute makes a specific exemption for rifles and shotguns provided the minor is following the age restrictions laid out in 29.304, and those restrictions only apply to those under 16. As he was 17, his possession of a rifle would be legal in basically any context where it would be legal for an adult to do so.

However, when we move from that specific situation to a more general idea of what's the prudent thing to do, you're in a much more secure legal position if you are defending yourself on your own property than you are if you go out as a self-appointed vigilante.

Castle doctrine. You're talking about castle doctrine. While you are technically correct in that castle doctrine would provide an affirmative defense for the use of lethal force inside someone's home (and car and place of business in the case of Wisconsin law) that might not have otherwise been protected, under Wisconsin law all that means is that the court can't take into consideration whether the defendant had an opportunity to retreat if the person or people the defendant used deadly force against had broken into or were in the process of breaking into the home, car, or place of business in which the defendant was located at the time deadly force was used.

All of this is laid out in 939.48, Wisconsin's self-defense statute. When evaluating a standard self-defense claim in Wisconsin, the question is whether the defendant "reasonably believes that such force is necessary to prevent imminent death or great bodily harm to himself or herself."

At the time of the 1st shooting, Rittenhouse was being chased by a mob. He tries to duck in between some cars when one of his pursuers pulls out a handgun and fires it into the air. It's at this point that Rittenhouse turns to see the first person he would shoot (Rosenbaum, 36) lunging at him. He fires at Rosenbaum four times, with one of the shots hitting Rosenbaum in the head, dropping him. Rosenbaum unsurprisingly die shortly thereafter.

There's a brief recovery period where his pursuers backed off and Kyle attempts to make a phone call. I would have assumed it was 911, though a news outlet claimed he called a friend. Then he starts leaving the scene and his pursuers start chasing him again. Now Rittenhouse is running down the middle of the street (after having been already hit by one of his pursuers), when he trips.

The first member of the mob runs up to him and tries to kick him in the head. It's not clear from the footage if he landed the hit or not, but after the kick Kyle shoots at this person and misses. While this is taking place, a 2nd person (Huber, 26) is closing in from another angle with his skateboard in hand. It looks like he's getting ready to hit Rittenhouse with it, but panics when he sees Rittenhouse shoot at the guy that tried to kick him, and the actual hit that lands looks pretty weak. It seems like Huber briefly tried to hold the skateboard with one hand while trying to grab his gun with the other before disengaging. Rittenhouse fires once, shooting him in the chest, with Huber running away and dropping a few seconds later.

There is also a 3rd person (Grosskreutz, 26) approaching with a pistol in his hand right behind Huber, who ducks and throws up his hands for a moment when Rittenhouse shoots Huber, before dropping his hands and lunging at Rittenhouse. Rittenhouse then shoots him once, hitting him in the arm. Grosskreutz then runs away clutching his arm.

What I haven't found is footage of what exactly went down that led to the mob pursuing Rittenhouse, so I can't say for certain if he did anything unlawful that might have provoked them. This matters because 939.48 has a section on how the issue of provocation by an unlawful act affects his right to claim self-defense. However, since Rittenhouse was fleeing the encounter, he likely would have regained his self-defense privileges under 939.48(2)(b), unless the prosecution can show that 939.48(2)(c) (which reads "A person who provokes an attack, whether by lawful or unlawful conduct, with intent to use such an attack as an excuse to cause death or great bodily harm to his or her assailant is not entitled to claim the privilege of self-defense.") would apply in this case.

Put simply, Wisconsin does allow for the use of lethal force in self-defense where there is a reasonable belief that a threat of death or serious injury exists, and being chased and attacked by an angry mob (and having cause to believe you had been shot at, to boot) would make that a reasonable belief. As in most states where the requirements are met, self-defense is an affirmative defense, meaning that if Rittenhouse's defense team can credibly show that Rittenhouse reasonably believed that he was facing a threat of death or serious injury, and that he reasonably believed that the use of lethal force was necessary to nullify the threat (and based on the footage I believe they won't have any trouble proving either of those), then unless he provoked them with the intention of creating a situation where he could use lethal force with self-defense as an excuse, he cannot be prosecuted.