Visiting Hong Kong, Beijing and Japan

Hello, I want to know how many Chinese entry permit I need for this trip:

1) I´m traveling from Brazil to China. I arrive at Beijing Capital Airport on 23rd December at 06:15 and I have already booked a flight in another company to Hong Kong at the same day at 12:15 (6 hours at the airport). Do I need an entry permit for this day?

2) On the 27th December I'll fly from Hong Kong to Beijing and will stay in Beijing until January the 4th, because on january the 4th I fly to Tokyo. For this period in Beijing I need an entry permit, right?

3) On the January the 13th I'll fly from Tokyo to Beijing, because my flight to Brazil departs from Beijing on January the 14th. Do I need an entry permit when I arrive in Beijing from Tokyo?

The question is, how many entrances I need to apply for the entry permit? Is a 2 entrance Visa enough for this trip?

Thank you very much for your help!