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I used to be on SO. For professional and personal reasons, I no longer am.
If Für Elise is in Am why there is a D# in it?
Yes, it's in A minor. Just check the beginning and the end of the piece. It's very obvious that it's in A minor. The fact that there are other notes does not change the key. It's not even a tonal excursion, let alone modulation. (In fact, it's very common to use the sharp fourth in minor keys. It's a good tool to make certain parts sound more "exciting", so to say.)
Cziffra's cadenza in Hungarian Rhapsody No. 6
I'm sorry, I may have been misleading with the wording. I am playing this on the piano. I've also found the PDF you linked to, and the original cadenza is not what Cziffra plays. If you listen to it, you will hear that the last part of the last bar is not a simple scale, but it goes up, down, up, down, and then up again.
Original underlying melodies of Liszt's Hungarian Rhapsodies
Thanks! I'll have a look at Bartók's book. As for the transposition, I'm Hungarian and I'm pretty comfortable with writing down folk tunes.