do we have enough time and do we need to collect our luggage in Beijing airport when transfering

For your cases, you may need to collect your luggage at PEK and recheck it again.
The Air China and Mongolian Airlines are two different airline companies and they do not cooperate with each other, so the passengers need to collect the luggage during the transfering.
But in order to make sure, you are still suggested to contact the airline company for consulting exact information.