Belgian citizen: Visa for Hong Kong with transit in Peking/Beijing

I still am guessing because I don't know which entry permit I need to travel as a Belgian tourist to Hong Kong.

I and my wife have a Visit for 7 Days in Hong Kong arranged by Flight.
We have a flight-transit in the airport PEK, Beijing/Peking (china).
I have reading on several sites that I do not need a Visa. I only need a Passport (valid for 6 months)
Is that correct?

When I do need I VISA, can you tell me precisely which entry permit I need to Arrange and how I can arrange this? Is this by internet or directly on the address from the Hong Kong Embassy in Belgium?
I am a citizen of Belgium.
My flight starts in Dusseldorf (Germany) and will end in the international Airport of Hong Kong (HKG).

Extra Info: The Transit in Beijing has the duration of 12 hours. Can I have a quick visit of the city Beijing or do I need than another Visa.

Thank you.
Jos De Roover