If you can't find criticism of the Chinese government on the internet, you haven't been looking very hard. Perhaps the internet in China is censored so well that none of the stories get through. I found a story right away from Human Rights Watch that details many of the protests and individuals who have been persecuted for their views. I will post just one paragraph from that article here.
From mid-2013, the Chinese government and the ruling Chinese Communist Party (CCP) have issued directives insisting on “correct” ideology among party members, university lecturers, students, researchers, and journalists. These documents warn against the perils of “universal values” and human rights, and assert the importance of a pro-government and pro-CCP stance. (Human Rights Watch. World Report: 2015. China.)
Your statement that "Majority of Chinese people don't care much about democracy" is impossible to verify objectively, since speaking out about lack of democracy could land you in prison in China. Take the case of Cao Shunli, who was imprisoned for trying to participate in the 2013 Human Rights Council in NYC. She died in prison after her jailers denied her medical treatment.
Democracy is not just a way to make free speech and freedom of association possible in a country. It is the only way. Many of the problems facing China involve a lack of concern for the environment, which leads to deaths from pollution. These kinds of problems can only be addressed by using freedom of the press (to publish stories critical of the government), freedom of speech (to let others know the truth about government policies), freedom of assembly (so that people may gather together and discuss alternative solutions), and freedom to elect the leaders of your choice instead of being forced to vote for the party's choice.
All of these freedoms are only available under a democracy. China will never be able to address its problems without them.