Singapore passport holders are exempt of visa to visit China mainland for less than 15 days. You may not need a visa to Guangzhou if you just stay there for a few days.

I'm not a Singapore passport holder. I hold a passport from Mauritius but I currently reside in Singapore. I am buying air tickets from Singapore to Hong Kong and Hong Kong to Singapore.
From Hong Kong, I will take the train to Guangzhou.
Can I apply for a China visa in Singapore even if I only have round trips tickets Singapore-Hong Kong-Singapore? It is not possible for me to buy train tickets of Hong Kong to Guangzhou from Singapore. I can only buy the train ticket when I reach Hong Kong.
What other documents will I need at the Chinese Embassy in Singapore?
Please advise. Thank you.

You can also apply for the China visa at the Commissioner's Office of the Ministry of Foreign Affairs of the P.R.C in the Hong Kong Special Administrative Region if you can't get your tickets booked in advance.