3 and 10 layover in Beijing?

A cousin of mine and me (we're both Americans) are thinking on going to Seoul but the cheapest flights are through Air China and have layovers in Beijing for 3 hours (going to Seoul) and 10 hours (leaving from Seoul). What would we need to be able to just stay inside the airport for the 3 hours and then for the 10 hour layover a week later, be able to explore a bit outside of the airport? Thanks in advance.