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G-flat minor is, as you note, a terribly awkward key, since its relative major is B-double-flat. That is, the third scale degree is enharmonically equivalent to A, but it's actually B-double-flat. That has nine flats in its key signature (or, actually, five flats and two double flats). F-sharp minor has the rather more normal relative major of A major, ...


Coda means "tail" in Italian. It's a tail-end part of a longer piece. A coda may be used however a composer wishes: to extend a cadence, to recapitulate some material, even to introduce new material.


TL;DR: It's just better to write since F♯-minor has a lot less signs to write than G♭-minor. The original tonality you listed was G♭-major; it has six ♭s. "Converting" major tonality to same-named minor one requires to flatten it triply: add three ♭, or remove three ♯s. (Of course, you should use circle of fifths; this is a ...

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