double entry into china

hi

i am a Singapore passport holder. I am planning to travel to China for about 13 days and take a train from China to Mongolia. After staying about 3 weeks in Mongolia, I will travel to Inner Mongolia for about 1-2 weeks.

Do I need any visa application when I re-enter into China / inner Mongolia ?

Also when I arrive in China, for purpose of free transit exemption, am I required to present an outbound transport document (train ticket or air ticket) to prove that I will leave China within the allowed visa-exempt 15 days ? As I will only purchase my train ticket to Mongolia after I arrive in China, I do not hold any outbound ticket, is there any other alternative document required for customs clearance?