Entering by Train, Exiting by Plane

Hello, I am planning to enter China on the Trans-Mongolian from Ulan Bator to Beijing.
Staying in Beijing for 3-4 days and then catching my flight to Europe.

Would that route be eligible to the 144h free transit?
I am mainly concerned about the inspection on the Chinese border...
Kindly clarify whether the application form will be submitted and processed at the Beijing West Railway Station (if I have understood it well...)

Many thanks!