Part of Hong Kong Basic Law (their Constitution, which was adopted during the handover process) stipulates that "the ultimate aim" is elections by universal suffrage for both the Chief Executive as well as the Legislative Council. So the demand for universal suffrage is simply asking the government to make good on their promises from 1990/1997.
One of the reasons that the extradition bill caused such an uproar in the city is that Hong Kong citizens are protected by rule of law in a way that doesn't exist in China. The law has clear definitions and punishment for rioting, and the actions of some protesters could very well fall into that category. So to ask for all rioting charges to be dropped is asking for the government to give in to mob rule. (Caveat—I don't think the rioting charge would be as big of a deal as it is if it didn't carry a 10 year prison sentence. But it's hard for the protesters to ask for anything less than blanket amnesty... Without looking at a specific case, where do you draw the line? What sort of punishment is reasonable?)