Visa-Free Transit in Shanghai (January) + 2 Visa-Free Transit in Beijing (April)

I can´t believe I've found your site, as I had nowhere else to ask this question on the net:
I am flying from Taiwan to Barcelona with a stopover of around 40 hours in Shanghai for which I´ve already booked 1 night accommodation, hoping that the visa-free transit should work for the 4 of us.
But then, we are flying from Barcelona to Hanoi with a stopover of around 20 hours in Beijing for which we will book a day tour from a Chinese company. And also, on the way back from Hanoi to Barcelona, we have another stopover of around 20 hours in Beijing for which we intend to get out and visit the city.
The airline for the 3 flights is Air China, our nationalities are Spanish, German and Argentinian, so the question is, are we able to enjoy the visa-free transit 3 times in less than 4 months? Are the 3 stopovers eligible for a visa-free transit?
Many thanks for the opportunity to post this question here, you are being very helpful.