How far in advance can we buy the tickets and are there roundtrip tickets for the trains?

We are a couple planning to travel from Beijing to Harbin via train on Feb 17 and from Harbin to Beijing on Feb 22 or 23 depending on which times are more convenient. We have a flight leaving from Beijing (PEK) at 5.50. Is there a ride that goes to the airport? If we purchase seat now, how will we receive them?