Can I apply for a 72Hrs free transit in Guangzhou airport? register in the police station?

Michelle, you mean your travel route is like Birmingham-Guangzhou-Amsterdam-Beijing-Hanoi? If yes, when you enjoy the 72 hour free transit in Guangzhou, you need to register at the police station within 24 hours. If you stay at a hotel, usually, the hotel will do that for you and you can confirm that with the hotel. If you stay at your friend’s home, you need to go to the police station and register on your own.
For your second transit in Beijing, you don’t need to do that.

Or you will travel like Birmingham-Amsterdam-Guangzhou-Beijing-Hanoi? If so, you cannot enjoy the 72 hour free transit. You need to apply for a tourist L type or transit G type in advance.