Am I eligible for 24-hour TWOV? My nationality is Indian and I am travelling from Australia to India

It would be a great detail if you have written the name of your layover city in China, but I will assume that this is Guangzhou or Kunming. If I'm right, you are perfectly eligible for 24 hour visa free transit any you don't need any kind of visa. As far as your exit from the airport is concerned, you are absolutely free to apply for a temporary entry permit upon your landing at 24 hour visa free transit counter. You have to know that the issuing of a temporary entry permit depends entirely on a discretion of immigration authorities on a day of your arrival. If you have a hotel booked through an airline, your chances will be very good.