1) That had never occurred to me - nice idea, though it's perhaps unlikely that Chopin would have had enough experience of trains to be aware of the Doppler effect from them. 2) Calculations of the Doppler effect give the relative change in frequency, so for a change of a semitone (or any inyterval) it doesn't matter what note you start with. In equal temperament a semitone corresponds to a frequency of the 12th root of 2 (because there are 12 in an octave, which is a 1:2 ratio), about 1.0595. Using the formulas from the website above, and bearing in mind that you have to consider the train both approaching and receding (so the "true" note, which you would hear if the train was stationary, is somewhere in between), I think that to give a change of a semitone the train would have to be travelling at about 10 metres per second (36 km/hour, 22.4 miles/hour). The calculation depends on the speed of sound, which can vary according to air pressure, and also wind speed, but I don't think these would change the answer much in the normal range of conditions.

For what it's worth, there's an answer on Stack Exchange that agrees with my calculation: "For a difference in frequency corresponding to a semitone ... the speed is about 36km/h"

Horses mate.