1. There will be no transportation after 23:00 for your use at the airport. Since you have four together, so it is also reasonable to take a cab to the hotel.
2. You couldn't purchase the train ticket at Pudong Airport. However, on the next day, you could go to any railway stations or ticket halls in downtown area to purchase train tickets. Usually, these trains could be purchase 20 days in advance, so it is suggested that you book the train tickets via some agents as early as possible.
3. Yes, the train code, room and bed No. will be indicate on the ticket. You could required the staff to arrange you four in a room. The D-train's ticket fare is about CNY450~550/adult, T-train's ticket fare is about CNY500/adult/soft-sleeper. It is suggested that you search the detailed info. on this website. You'd better get to the railway station 1~1.5 hours in advance.
4. After arrive Beijing, please take a taxi to the hotel. The fare is about CNY25~35.