Hong Kong, Seoul and possible stop in Beijing

Hi,

We were wondering whether it would be possible to fly from Hong Kong to Seoul via Beijing (with a 72-hours exemption), stay in Seoul for a couple of days and then back to Europe via Hong Kong this summer. Would this be possible under the 72-hours exemption program, and if not is it possible to apply for a Chinese visa in Hong Kong or in Singapore (where we will be before Hong Kong)?

Thanks.