CPH-> PVG (Shangai) 20 hours -> Tokyo and then on the way back Tokyo-> Bejing 21 hours -> CPH

Radoslaw, there will be no problems at all. You will do the following:

1. Print out your flight tickets and your hotel booking confirmations and have them with you at hand.
2. On board of plane there will be arrival/departure cards dispensed. Fill out one and for the purpose of your stay in China tick the transit box.
3. Upon your landing in Shanghai and later in Beijing, you will first approach 24/144 hour visa free transit counter where you will apply for a temporary entry permit by presenting those printouts. This application is free of charge.
4. After your permit is granted you will cross the immigration and proceed to the city on your own.

Basically, this is it.