Presenting the ticket for flying to a third country

Hi, I would like to visit Beijing with the 72 hours visa. I would fly from Hong Kong to Beijing, and then form Beijing to a third country. I have been told that when I present my flying ticket to a third country, all the flights (Hong Kong-Beijing and Beijing-Third country) must be on the same sheet, like an unique trip. Can I not buy the flights separatly?

I have been also told that that i can not leave the district of Beijing with the 72h transit. Could I visit the great wall?

Thank you in advance