1

>>"Will we be able to leave the airport for sightseeing in Shanghai without having a visa? We all have german passports."

Short answer is "yes."

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Here's a source. The website has some additional questions and answers:
http://www.shanghaihighlights.com/shanghai-tours/visa-free-travel.htm
(Note: It also has some advertising. I am not affiliated with them in any way.

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Restrictions of the 72-hour Visa-free Transit

The 45 visa-free countries are: 31 European Union countries (Austria, Belgium, Bulgaria, the Czech Republic, Cyprus, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Poland, Portugal, Romania, Russia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Ukraine and the United Kingdom), 6 American countries: Argentina, Brazil, Canada, Chile, Mexico, and the United States, and 8 Asian/Oceanian countries: Australia, Brunei, Japan, Qatar, New Zealand, Singapore, South Korea, and the United Arab Emirates.
This regulation does not apply to passengers who travel on a return flight (e.g., Hong Kong – Shanghai - Hong Kong). The Shanghai stopover must be a transit point between two different cities. Visitors returning to same city as they departed must apply for a visa in the normal way.
The 72-hour visa-free stay only applies to transit via Shanghai Pudong and Hongqiao Airports. Passengers arriving by train, ship or any other method should apply for a visa in advance of arrival.
Visitors are not permitted to leave Shanghai to visit other cities during the 72-hour visa-free period. Departure must be via Shanghai from Pudong or Hongqiao Airport.
If visitors are unable to depart on time for unavoidable reasons, such as flight cancellation or treatment of sudden disease, should apply for a visa from Municipal Public Security Bureau (PSB). Extensions are not available for the 72 hour transit visa.

2

yes, no problem. Be sure to go to correct passport/immigration line to get transit stamp and exit airport.

3

Make sure to print your onward tickets ahead of time.

4

Yes, i confirm that you can visit Shanghai according to the new China-visa free policy. I saw this in chinatour.com accidentally and was told that visitors are visa-free to travel Shanghai within 72 hour transiting time. According to the information provided, German is the visa-free one among the 45 countries.

According to the information provided, foreigners holding third country visas and confirmed onward air tickets can now apply for a 72-hour visa-free transit at Shanghai Pudong International Airport or Shanghai Hongqiao International Airport. The 72 hours will be counted from the moment visitors obtain their transit permits, but not the time when they land at the airport. Tourists need to register at a police station with their transit permits within 24 hours after entry.

Hope it helps.

5

Only need to register at the police station if you stay with a friend rather than a hotel.