Can I wait at Guangzhou Baiyun Airport until morning?

1. Yes, you can stay at CAN until morning.
2. There are four trains each day: 19:30, 19:35, 20:40, and 20:45. The first two are bullet trains, and the duration is about 4 hours; the last two are ordinary trains, and the duration is 12 to 13 hours.

I am sorry that there is no train service at midnight. You are advised to take shuttle bus line 1 to Civil Aviation Office (Main Railway Station). The buses operate until flight finish by the way. Then, stay at the hotel near Main Railway Station, and tour around downtown area. On the next morning, you can go to see Haizhu Square, Pearl River, Beijing Road Pedestrian Street, Canton Tower, etc. In the afternoon, you can take a train to Xiamen.

If your itinerary is tight, just take a direct flight to Xiamen directly (about 1.5 hours). :)

Thanks for the prompt reply. your infomations helps and greatly appreciated.