How can I transit from terminal 3 to terminal 2 and stay one night in the Beijing airport

If you has the connecting flight or using the flights of the same airline company, it is no need to claim your luggage. But in reality, different airline companies have different rules, so it is suggested to confirm from the airline company directly.
For staying one night at PEK, you can stay one night in T2 and u can choose to live in the hourly lounges for a night.