My flight arriving after midnight at Shenzhen. Can I just stay overnight at airport?

Yes, you can stay overnight there. You may take a rest at the chairs in the waiting area, or stay at the nearby hotels. For instance, the Airport Hotel is a nice choice for you. It is located at No. 1028, Jichang 6th Road, Baoan District. It is to the opposite of the terminal building. A standard room costs about CNY 200 per night. You can book a room by dialing 86-0755-27772888.