I'm a lawyer, and from what I have seen I highly doubt Rittenhouse will be convicted of any homicide charges. The fact that he shouldn't have been there, the fact that he was inciting trouble by his mere presence and even the fact that he was illegally in possession of the gun will not be factors because they don't have bearing on self-defense. Self defense is all about the moment, and whether the defendant had a reasonable fear that he would be killed or suffer great bodily harm. In both shooting instances, Rittenhouse is running away and being pursued by a large group. In the first, a gun goes off behind him just seconds before he discharges his weapon at a man (who I believe was armed) and had gotten close enough to him to grab the barrel of his gun. In the second shooting, moments later, Rittenhouse is clearly being chased an attacked by a large group and I think in reasonable fear of great bodily harm.
The only way he gets convicted is if the State can show that in the first shooting, the people attacking him were themselves acting in self-defense against him. From what I've seen, that is a little far fetched, as he is running away, gun barrel down. It will take more than just showing he had a weapon, there will have to be evidence of him brandishing it and threatening people. That isn't in the evidence that's out there now, but it could emerge. Ironically, whether the second shooting is lawful may depend largely on whether the first shooting was self-defense. If Rittenhouse is fleeing after what has been determined a justified homicide, then the crowd has no right to attack him, and his use of force against them is now lawful. However, if the first homicide was not justified, then one could conclude that the crowd was acting in self-defense (or defense of others) when then chased him down to subdue/disarm him.
All in all, I think there is far too much gray area for a murder conviction. All it takes is one juror to vote against, and I think there will be more than that. He will definitely get convicted of some lesser charges though.