About Kirito's priorities... he is not just a 16YO kid, but the 16YO that saved 2K players from SAO... he already used that to find Asuna IRL through the police. He also needs no evidence to Asuna's father worried, the police interested, and Sugo's competitors digging dirt. As for how he can make the connection between Sugo and Asuna's captivity in Alfheim:
Asuna is still plugged in a game
Sugo told him it's convenient for him
He sees a photo of Asuna in Alfheim
Sugo own the Alfheim company
But instead of doing something IRL about it, he goes to play the game, and as of last episode, not even play it to save Asuna in game
