According to this site...

http://open-site.org/Business/Transportation_and_Warehousing/Aviation/History/1940_to_Present/

...regularly scheduled coast-to-coast commercial airline service began with DC-5's and Lockheed Constellations on March 1, 1946, fairly close to Hagen's coast-to-coast flight in August 1945. Same site says Flying Tiger Lines began coast-to-coast freight service in August 1945. Perhaps Tom's grateful Pentagon contacts (mentioned in the novel) got him a seat on one of those Flying Tiger flights in August 1945.

As for the headless horse: Tom obviously met with Vito and Sonny as soon as he returned from California. But neither the movie nor the novel says that Luca hit the horse immediately--or even that Luca himself did the dirty deed. Soon, certainly, because Johnny said that filming would begin in a week or so. But, perhaps Luca subcontracted the job to one of Vito's labor contacts on the Coast.