Are augmented sixth chords always in minor?

An augmented 6th is an augmented 6th, and can be used in both major and minor keys. It's generally used in predominant function. In the key of C, you'll usually find it as Ab C F# (Italian), Ab C Eb F# (German), or Ab C D F# (French). With all three cases, the F# resolves up and the Ab down to form an octave.

The first chord is the fully diminished seventh of B minor - A# C# E G The second chord is V7 in D major - A C# E G resolving to D F# A. The way to make this an augmented sixth chord is to respell the seventh as Fx and resolve it to G# major or minor. G# B D A is almost a fully diminished seventh chord - I would probably analyze it as either G# diminished with a minor ninth, or as Bm13 (B D [F#] A G#). There are no augmented sixth intervals in this chord. I think you're a little confused on augmented sixths - here's a quick example: In C major, G B D F functions as V7 or the dominant seventh. If you keep the same sounding notes and enharmonically respell the seventh (F) as E#, it becomes a German augmented sixth chord that traditionally resolves to F# major or minor. The augmented sixth (G - E#) sounds like the interval of a minor seventh, but does not function in that context.