72-hour free transit in Beijing

First of all, thanks for answering all these questions!

I'm planning to book 2 return tickets (with different carriers), one from London-Beijng (via Dubai) between 1 July and 4 August and a return ticket from Beijing to Perth (via Kuala Lumpur) between 3 July and 3 August. Before travelling onwards to Kuala Lumpur/Perth, I would like to stay 2 days in Beijing. Am I eligible to get the 72-hour free transit in Beijing (even though I have 2 different return tickets?). If I am eligible, is it possible to visit the Chinese Wall? I read that one can only stay in Beijing, not sure if visiting the Chinese Wall falls within the limits of this type of 'visa'.

Thanks for helping :)