8 hour layover

I am flying from Los Angeles to Thailand, by way of Beijing. I have an 8 hour layover on the way to Thailand and an 8 hour layover on the way back to Los Angeles.
1. Do I need to file for a transit permit in advance of my arrival at the airport?
2. Am I able to get a 72-hour permit for both layovers?
3. If I'm only in Beijing for 8 hours, do I still need to register with the police department?
4. Does the 72-hour permit cost anything?