I am Singaporean citizen and want to go to China for 10 days for tourist purposes. Do I need a visa?

Do I need to make a payment of $25 at the airport to enter China?

I have booked a flight from Hanoi to Ho Chi Minh city 13 days after I arrive in China. I plan to enter Vietnam overland (bus/train) from China, but this has not been booked. With proof that I will be leaving China within 15 days, do I still need to show a departure ticket out of China of some sort?

Will this pose any problems?

Thank you.