Can i apply for the 144 hour transit?

Hi,
could you please help me to clarify if i am allowed to use the transit opportunity, if i fly from Rome to Shanghai, stay there 2-3 days, then on my flight back to Rome, i have a stop of 2-3 hours in Dubai?
Once staying in China, Shanghai would i have the opportunity to fly to Beijing and leave the country from there?
Thank you a lot in advance.
E.