A: [Is] the right hand part as based on an Hungarian Gipsy scale?
No. Both the right hand and left hand comprise an elaborated fully diminished seventh chord; specifically, the viio7 chord in D major —
C# E G Bb.
In the excerpt below, the full-size notes are all part of a C#dim7 chord. The small notes are accented chromatic lower neighbors to the third note of each triplet grouping.
The effect is a three-voice texture in which the second (highest) notes of each triplet comprise the top voice, the first and third notes comprise the middle voice, and the left hand makes the lowest voice.
Note that you are correct to describe the beginnings of each triplet as dissonances, but incorrect to describe them as minor sixths. G-D#, for example, is an augmented fifth — a dissonant interval. It's enharmonic equivalent, G-Eb, is a minor sixth, which is consonant. This difference in how the same pitches sound in context is why the spellings and interval labels are different.
Also, to characterize this section as a scale would be incorrect. It is an arpeggio that includes a series of non-harmonic tones. However, as a tangential point, the notes involved make up a whole-half diminished (octatonic) scale rooted on C#.
B: [Why go] through 140-143, announcing come back on theme from 144?
There is a lot going on here. Locally, these measures represent a "cooling off period". Notice that in mm. 136–140 the left hand shifts from eighth notes to quarter notes, then in mm. 141—143 to a multimeasure sustained octave. At the same time, the right hand is shifting from wide intervals (sixths) descending over three octaves (mm. 136 – 139) toward much smaller intervals that remain at the same octave.
Harmonically, Brahms also uses this time to shift from the fairly ambiguous diminished seventh chord to the more "certain" dominant seventh chord, easing us gently into the main theme.
A full analysis is beyond the score of the site, but would involve noting the balance between sections, the harmonic relationships, thematic relationships, etc.
C: Why ... do I get the impression that it's the left hand going down a perfectly legit D minor?
Why one might hear it as a D minor arpeggio seems very odd, but hearing it as being in the key of D minor makes perfect sense, since that's exactly where we are. The dissonances that occur each half-beat are due to the lower neighbors described in part (A) above.