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Great questions Vadim! I always found it helpful to analyze the progressions of the chords and think by numbers. For example if the tune starts out 2-5-1-6, then I know I just have to play a 2-5-1-6 in another key. I try to do the same thing for melodies. Figure out how the notes relate to the chords by numbers. So if the melody outlines the chord 1-3-5-7 then I can just play that same sequence of notes in another key. It is quite difficult to get the hang of and even I have to practice quite a bit to do this! Hope this helps!