if you have a short layover on transit in beijing, such as for 8 hours from 12.30 to 20.30, how not to be refused by the immigration and customs?
While getting out of the airport on this relatively short transit isn't guaranteed, you can improve your chances by not admitting that you want to go sightseeing in the city, and instead saying you just want to get a better lunch than the choices available in the restricted airside terminal. Once stamped in at the TWOV queue, there is nothing to keep you from leaving the airport. Another excuse that has worked for others, is that you want to step outside the terminal to have a smoke, as Beijing airport is 100% indoor smoke-free.
if you are eligible for the 24-hour Transit Without Visa. That guarantees you transit through Beijing airport but doesn't come with automatic privilege to leave the airport. However, if you approach the TWOV queue (where you ask for permission to leave) and show a nearby hotel reservation "to allow the kids to get some rest after the long international flight" then you have a decent chance of being allowed to get your temporary entry stamp and leave the airport. Just make sure it is a hotel in reasonable proximity to the airport, not a central Beijing hotel. The officer wants to be comfortable that you are going to return to make your onward flight out.
The longer the transfer time, the higher the chance of getting the clearance. But there are no fixed rules. With 10 hrs, I would just give it a try.