Would anybody know the parent major scale of F sharp minor 7 flat 5?
There are two likely choices for the parent scale of an F♯-7(♭5) chord, also known as an F♯∅ or half-diminished chord.
This chord can be built on the seventh degree (or the Locrian mode) of the major scale, meaning that G major could be thought of as the parent scale for this chord. From F♯ Locrian this gives:
F♯ A C E G B D 1 ♭3 ♭5 ♭7 ♭9 11 ♭13
But you can also build this chord on the sixth degree (or the Locrian #2 mode, or the half-diminished mode) of the melodic minor scale. This would make the A melodic minor scale a parent scale of the half-diminished chord. From F♯ Locrian #2 this gives:
F♯ A C E G♯ B D 1 ♭3 ♭5 ♭7 9 11 ♭13
Note that the only difference between these two approaches is in the 9th. The Locrian mode from the major scale provides a lowered 9th; this is sometimes called an "avoid" note since it is a half-step above a chord tone and is harmonically unstable. The Locrian #2 mode from the melodic minor scale provides a natural 9th. None of the upper extensions are a half-step above a chord tone, so there are no "avoid" notes here.
The most common usage of half-diminished chords (min7b5) is as the ii chord in a minor key. In that regard, the parent scale of F#min7b5 is E minor, which, of course, is the relative minor to G major, where F#min7b5 is the vii chord.
A characteristic use of the half-diminished chord is within a ii-V-i chord progression. Here's a classic example: the beginning of the bridge in "Autumn Leaves":
In G Major (Ionian mode) the F♯ is the 7th scale degree. It is best to keep it simple, you could analyze it forever. I suggest grabbing your instrument and practice. Make music, regardless of what scales are available and where it is derived from, play, have fun and don't over think it. Enjoy and you can find a parent scale from one chord. Absolutely.