Is Hong Kong included in the 72-hour Visa Free Transit? Could we get stamp at transit counter?

HK is not included in the China mainland 72-hour free transit.

Do you make a transfering in HK? Based on the policy, USA nationals can enjoy a 90-day free entry. So you can only use your passport to enter HK. If you only transfer at HKIA, you will get a slip for transfering with your passport.