Most of the common people look more shocked than sad. The only ones actually crying are the people that personally knew Sabo like Dadan and Makino which makes sense as they're basically parent figures to him and will obviously be surprised if he's convicted of murdering a famous King and abducting his daughter. Even in the anime, the civilians crying were from Alabasta which makes sense as they lost their King.
False, Dragon is just afraid because of the news, not because of him not reporting. Secondly, he's on the run, of course, he can't contact them at the moment, at least according to the theory. And this theory being true makes a lot of sense too in comparison to Ace 2.0.