Does my family qualify for the 72 hour visa?

Hello there,

Was wondering if you could kindly clarify some things for me. I want to be sure my family qualifies for the 72 hour free transit.
My son (Ethan, age 6) and I James Tengelis are Canadian
My wife is American (but lives with us in Canada)
We are going on a trip to vacation in Asia in March of 2016. Trip is for pleasure only.
We are going from Canada (Toronto)-India-Nepal (Kathmandu)-China-Beijing-Canada (Toronto)
We fly to Beijing from Kathmandu, Nepal, arriving at 12:20 am on March 26, 2016. We are staying three days (officially less than 72 hours). Our flight departs from Beijing International on March 28th around 6 pm (1800). So less than 72 hours. We arrive at Beijing International and depart Beijing. We will NOT be visiting any other cities in PRC-just Beijing. Purpose of our trip is only site seeing.

My question is this:
1) Do we ALL meet with the conditions of the 72 hour free transit??
2) Do we just get this free transit service at the airport in Beijing upon arrival? OR DO WE NEED TO DO SOMETHING IN ADVANCE FROM CANADA OR USA (in the case of my wife)?
3) Is there any fee for this 72 hour free transit at the airport or otherwise?
4) Do we need to register or visit a police station because we are staying longer than 24 hours? Or can our hotel do this for us?

Any other advice you can provide us with is much appreciated!

Thanks so very much!