Connecting flight in Shanghai for 72 hr TWOV in Beijing.

I am a US citizen. I would like to travel from NYC to India with a 72 hour Stopover in Beijing. My flight would land in Beijing on December 3rd, 2017 at 9:25am and leave from Beijing on December 6th, 2017 10:40am

My inbound ticket between New York & Beijing and my outbound ticket between Beijing and Delhi have a connection in Shanghai. Would that be a problem? Or, will I be allowed to check my baggages through to Beijing and Delhi respectively without requiring me to go through Immigration at Shanghai?

Also, since the 72 hour period starts at the midnight of the day I land, can I stay an additional night and leave Beijing on the 7th instead of 6th December?