Singaporean baby born in China

Hi, i'm a Singaporean and my baby is born here in China last week. I'm registering my baby as a Singapore Citizen through the Singapore Consulate-General in Guangzhou next month. I have a query, after registering my child's singapore citizenship, it would take another 2 to 3 weeks' time to apply for Singapore passport. This means that my Child would not be able to travel out of China after 15 days. My understanding is normally, a Singaporean can only stay in China without any visa for 15 days, i am not able to apply for Visa for my baby as we need time to apply travel documents.
Is the 15days' restriction only applicable to visitors when they enter China and not applicable to foreign babies born in China so long they do not leave the country?

Next question: How soon can a Singaporean do a exit and re-entry into China after staying in China without Visa for 14days.

Thanks