Arrive via Hong Kong okay? Arrive via train, depart via air okay?

Am I able to enter Beijing from Hong Kong, and have Hong Kong count as my "Point A". So my intenerary would be as follows:

Leave by air Hong Kong Dec 11 at 12:30 -- Arrive Beijing Dec 11 3:40 PM
My 144 hours would then begin 00:00 Dec 12, correct?
So I would need my outbound flight from Beijing (to the US, in my case) to depart by 23:59 on Dec 17, correct?

Can I arrive to Beijing by train and depart by air out of PEK? Or if I arrive by train must I leave by train? So, must I arrive and depart via the same kind of transit (train or air, not both)

Sorry for so many questions, just want to be sure I am following the rules before I spend a lot on tickets.

Thanks!