I am Canadian citizen living in Singapore with a dependant pass, do we need a double entry visa to go to Hong Kong, Beijing and Haikou?

Hong Kong is considered as a third territory in terms of visas and Canada passport holders are allowed to stay in HK for up to 90 without a visa, for the purpose of tourism only.
One entry is enough if you visit Beijing and Hainan continuously , for they are both in China mainland. But if you'll visit in this order, Hainan-HK-Beijing or Beijing-HK-Hainan, double entries will be needed.
Your passport are OK if applying for a one-entry visa. Usually, the passport is required to have at least 6 months validity when submitted for visa application.