You can argue that it was not prudent for him - or anyone - to be there, but you cannot argue that he had no right to be there. He had the exact same right to be there as all the protesters, and much more right to be there than any of the rioters and arsonists, including the arsonist who initially attacked him.

There is no evidence that Rittenhouse did anything to invite the initial attack against him. "Carrying a gun" is not, in and of itself, a justification for someone to attack the carrier.

The event happened in Kenosha, Wisconsin. Not Washington.

The law in Wisconsin actually did allow him to possess and carry a rifle at the time; the way the law prohibiting minors from carrying weapons was written, he could only have violated it if he was illegally hunting. It's a rather technical point that the Wisconsin legislature probably should have corrected, but the judge dismissed the charges because the law did not actually prohibit him from carrying the rifle.

"Duty to retreat" would not have played a part in the Rittenhouse case: he was on video retreating from all three of the people he shot, as well as a fourth person who he attempted to shoot, but missed. The first attacker was in contact with the rifle as Rittenhouse was running backwards from him. The next two attackers attempted to jump him after he had fallen. The fourth had a gun in his hand with his hands up, indicating he was not a threat. Rittenhouse initially held his fire. However, the final attacker suddenly pointed the weapon and lunged toward Rittenhouse.