Hong kong-shenzhen and Hong Kong-Guangzhou within 144 hours

Yes, you can travel in and within China as you wish. As far as you know Singaporean citizens do not need any kind of visa because they are allowed to enter and stay in mainland China for up to 30 days visa free. Your passport is all you need. Just forget about 144 and similar visa free transit schemes because they are not related to the citizens of countries that do not require a visa to visit China.