Yes, Sharps are the correct route. Gmin is the one quirky scale in our Major/Minor system in that it contains both flats and sharps.
All diatonic scales (our normal Major and Minor scales) contain 7 notes, one for each letter of the musical alphabet. If a letter is used twice, it is no longer diatonic.
The basic layout for any G scale is G A B C D E F G
Now of course to make it Major, we raise the F to F# which is the leading tone (It "leads" to the tonic) so G major looks like this: G A B C D E F# G
The telling note that determines major or minor is the third (B in this case). If the B is Bb then it is a G minor mode.
Convention has said that the Natural minor or Aeolian mode is the sixth mode of the major scale a minor 3rd above the root (relative major). Therefore convention has placed G minor with the same key signature as used for Bb Major.
G min (natural) looks like this: G A Bb C D Eb F G. But the natural minor scale leaves us with a Vm7 chord (Dm7, not D7) so the powers that be raised the 7th degree so that it would again become the leading tone. F becomes F#
This is the Harmonic Minor: G A Bb C D Eb F# G. This gives us a dominant V7 (D7). If we were to call it Gb, we would have 2 G's (an octave and a diminished octave) and no F.
But all was not completely well for the Harmonic Minor then left us with an augmented 3rd between the 6th and 7th degrees (Eb - F#) which some folks thought was unsingable and possibly the Devil's work -- the early church was neither fond of augmentation or diminution when it came to harmony and melody. So, the powers that be decided to raise the 6th degree (Eb - E) which gives us the ascending melodic minor: G A Bb C D E F# G. The descending scale when using melodic minor is usually the natural minor.
Of course, it took a long way around to get there when all they had to do was just change the B to Bb in the major scale and be done with it.
Now, as far as the spelling of the D aug 7 # 9.
Chords in tonal harmony are based off of stacked thirds (exceptions are the sus 4, add 2, add 6), so the basic layout for any D chord is D F A C E G B (1 3 5 7 9 11 13) In this instance, we are faced with a dominant chord to the 9th (to E)
The basic dominant 9 - D9 (or D7 with an added 9) is D F# A C E. Now we follow the instructions -- augment means to raise the pitch -- in this case the pitch to be raised is understood as the 5th or A becoming A# (Bb would be the b6 or b13) and # the 9 which is also raising the pitch so E becomes E# (F nat would be the minor 3rd not the raised 9). The proper spelling is D F# A# C E# and it contains the three elements that identify it as the dominant of G major or G minor -- D (the V) F#(the leading tone) and the C (making the tritone with F#) The natural resolution of a tritone with this spelling is F# up to G and C down to B (or Bb in G minor).
The instructions Aug and # always mean to raise a particular scale degree which either is to # a natural, ## a # make natural a flat, or make bb a b. Dim or b always means to lower a degree which means to make b a natural, make bb a b, make natural a #, or make # a ##.
Your chord is also sometimes written in lead sheets as a D7 #5 #9 or even D7alt. The improvising scale commonly associated with it is the Diminished/Whole-tone (sometimes called the altered scale) which for D is thus:
D Eb E# F# G# A# C D
1 b2/b9 #2/#9 3 #4/#11 #5 7 1