Hi, I'm a Singapore citizen, and would like to go to Zuhai for visiting and from Zuhai I would be go

Yes, you can do all the mentioned. You don't need any kind of visa or anything else because Singaporean citizens are allowed to travel to China visa free for a duration of stay for up to 15 days. In other words, if your stay in China will not exceed 15 days, you will enjoy your stay there absolutely visa free.