Hi, I am an Australian citizen travelling in Italy.

Miranda, usually, the residence permit in Italy will be required if you want to apply from there. But you can have a try if you can provide valid entry permit for Italy.

Would you mind explaining how the 144 hour free- entry works?

For example, you fly to Shanghai from Australia, after staying there for less than 144 hours, you will fly to HK, and then return to Australia from HK. In this case, you are eligible for the 144 hour free transit in Shanghai. And during the 144 hours, you are allowed to travel around Shanghai, Zhejiang or Jiangsu.
So if you want to use the 144 hour free transit, after staying in PRC, you should make sure that you will not fly back to the last country you fly in, but fly to a third country or region. Please note that the 144 hour policy is only carried out in Shanghai, Zhejiang and Jiangsu currently.

144 hours
Thank you for replying! Okay so for the 144 hours I don't need to apply for this prior to my arrival to Shanghai as long as I have a flight booked to leave Shanghai within 6 days to another country?