144 HR VISA FREE

Hello,

I'm going on a cruise with my aunt and the departure is at Tianjin port.
My itinerary is as follows:
I leave Paris on October 4th and I arrive in Beijing on October 5th.
I stay in Beijing from October 5th to October 7th.
The start of the cruise starts on October 7th from Tianjin Port.
October 8 Fukuoka Japan (1 day)
October 11 Taipei Taiwan (1 day)
October 13th and 14th Honk-kong (2 days)
That's my question:
I see that I make 3 entries in China. I wanted to know if I am eligible for the 144-hour transit visa upon my arrival in Beijing. I make a one-stop stopover in Taiwan, as well as a stopover in Honk-Kong.
Do I have to apply for a visa for China?