The basic scale here is known as maqam Kurd (or more precisely, Hijaz Kar Kurd) in Arabic music. In scale terms, as others have noted, it corresponds almost exactly to a Phrygian scale: 1 m2 m3 4 5 m6 m7 8. In practice, it has a number of other characterstics beyond the scale description.
As you noticed, there is a M6 used around 0:12. For comparison, if you listen at 0:19 there is a neutral 6th (1/4 lower) followed by the usual m6 at 0:20.
In theory terms, the M6 is a temporary leading tone to the m7 degree. The neutral 6th is the third of a brief detour into jins Rast on the 4th degree (Rast is 1 2 n3 4 5, so in context this is 4 5 n6 b7 8). The m6 brings us back to the parent maqam.
At 0:23, you hear a M2, similarly used as a temporary leading tone to the m3. He does it again at 0:51, 1:34 and 1:41.
At 1:35 and 1:42 the d5 (not #4, as the 4 is part of the melody as well) is a common descending cadential figure. He explores this more fully around 5:10.
At 1:56 there is a subtle microtonal shift to a jins called Jiharkah. It is very close to the first 5 notes of a major scale, however, the 3rd and 4th degree are lowered slightly (between 1/5 and 1/8 tone). So hear we hear a 6 that is slightly lower than a M6 and a 7 that is slightly lower than a m7. But not lowered a full quarter tone. He changes this back to n6 and m7 around 2:08 (leading up to the octave). He then proceeds to play with this sound, going back and forth a bit between the different sounds.
At 5:18, there is a similar figure to what you heard with d5, but using the d4 degree (effectively M3, but the m3 is also included). The 1 m2 m3 d4 jins is known as Saba Zamzama. ("True" Saba has a n2, the version with a m2 is what makes it "Zamzama"). At 5:32, there is a shift to Saba on 8. This has the structure 1 n2 m3 d4 (or 1 n2 m3 M3). This continues until 5:47 where he uses the M6 again as a leading tone that sets us up to hear the b2 (actually b9 here).
From here he establishes Rast (1 2 n3 4 5) on 4 more fully, giving us 4 5 n6 b7 8. He uses this to expand to a full maqam Suznak on 4: Suznak is Rast + Hijaz (1 m2 3 4) on 5. So we end up with 4 5 n6 b7 8 m9 10 11, locally sounding like 1 2 n3 4 5 m6 7 8.
The m2 and M3 in hijaz are narrowed, with the m2 about 1/8 tone higher and the M3 about 1/8 tone lower than their equal tempered counterparts (JI aficianados may notice this is close to ideal JI ratios for these notes).
I could go on, but this should give you a good sense of what to listen for and how much is going on. In this piece, we have heard 4 different 6ths, 4 different 2nds/9ths, and 2 different 7ths, as well as chromatic alterations to the 3rd and 5th.