Same qustions as most above - 4 days but less than 72 hours in Beijing

My wife, daughter and I will be departing LAX and arriving in Beijing on July 15th at 9:15PM, and departing Beijing on July 18th at 10AM for Hong Kong.

While I have a valid visa for China, it sounds like my wife and daughter can avoid it and utilize the 72-hour transit free entry process, is that correct?

From other posts, it sounds like we need to:
1- Notify our ariline that they will be entering on a 72-hour transit free stay (Is there any paperwork or form available?)
2- Complete a 72-hour free transit entry form on the plane (I have never seen these, but if not available on the plane, can we assume that they would have them at immigration at the airport?)
3- Register at our hotel once we check in? (I am not sure what this is for or what it entails, can you explain?)

Thanks for your good advice, it looks like you have a great website.