Can i take a flight from Japan to Mongolia stopping in 2 airports in China without visa???

Hello, i will visit Mongolia from Japan with Air China, the flight is CA954 from Fukuoka (Japan) to Dailan,1h connect in airport and then Beijing waiting 13h connect in airport to take the flight CA901 to Uluaanbataar(Mongolia). My questions are very simple:

1-Do i need VISA to stop in China???
2-My passport will be stamped at any aiport(Dailan or Beijing) in my journey to Mongolia))).

I am from Spain and i have many flights with layover in China and i just go through security without stamp my passport because was transit but at this time i will go first to Dailan and then Beijing(national flight) so i feel worry if i should go to Customs first and stamp my passport because i haven't enough page to be stamped, that's it.

Thank you for your answer