Nice discussion of the diminished scales. Just a couple observations. 

Triadic harmony and quartal (or quintal) harmony are based on different
understandings of music structure. They're not exactly inter-changeable. Melodies that are western in origin (at least from the 16th through 19th centuries, and most from the 20th century) come out of a triadic understanding, so the melodies imply triads. (This includes European modal music, what is
sometimes called "tonal" but is now more accurately called "functional" harmony, and the folk music of western culture. American folk music has some input from African and Eastern Europe, so there are occasional tunes that are atypical of either modal or functional structure.) You can often play open fifths or
fourths on one instrument while others are playing triads, but what you're really doing is playing part of the chord everyone else is playing and
adding some additional notes (extending the triad, or simply adding
dissonances). Remember that if you are in an ensemble setting, what is happening musically involves the sound of the entire ensemble. Of course, you can harmonize any melody anyway you want, and using non-triadic harmonies under triadic melodies can produce some very interesting sounds. That's what modern
composers who use folk tunes regularly do. (Sone of the most accessibly illustrations of this are from the work of Aaron Copeland.) A lot of "authentic" Appalachian folk music sounded quartal harmonies, at least in places, but this is almost always the result of pedal points (drones are the most common form of
pedal point). It has, however, left the music, and bluegrass after it, with a heavy use of added 2nds (or 9ths), especially in the subdominant and dominant chords.

It is the 3rd of a triad that determines if it is major or minor. So if
there is no 3rd sounding, it is neither. However, the ear will hear open fifths as a triad if it is expecting a triad to sound. Also, a "chord" that only
has two different notes is not technically a chord. It is an interval. Octave duplication in not a different note.

The closer the pitches are together, the "muddier" the overtones are. That's why open fifths (power chords) work so well in music that has a heavy use of distortion.

The term "pentatonic scale" refers to any scale that has only 5 notes from octave to octave. There are many pentatonic scales. The two most common pentatonic modes (patterns) in western music are called simply the "major pentatonic scale" (whole step, whole step, minor 3rd, whole step, minor 3rd) and the "minor pentatonic scale" (minor 3rd, whole step, whole step, minor 3rd,
whole step). The minor pentatonic scale is also called the "blues scale". The blues scale, however, often has a 6th note added (called "the blue note") between the 3rd and 4th pitch of the scale (this would be the same notes as the 4th and 5th pitches of a major scale of the same tonic) making the pattern "minor 3rd, whole step, 1/2 step, 1/2 step, minor 3rd, whole step". Obviously, this is no longer a pentatonic scale. If you add a note that is 1/2 step
below tonic (a B note in a C minor pentatonic scale, for instance) you
have added a leading tone and are now using either the melodic or harmonic minor scales (you don't have to play every note in a scale to be using that scale) and you are implying functional harmony. If you raise the second note of a minor
pentatonic scale (an E natural in a C minor pentatonic scale, for instance) you are now using a major scale of some sort. It is the presence of the minor 3rd that makes it a "minor" scale. Modes are classified as "major" or "minor" based on whether they have a major or minor 3rd in relation to tonic. (If you play both the major and the minor 3rds with other notes in between, you are simply
changing scales. If you play them consecutively, 99% of the time you are playing a major mode with a minor 3rd as a passing or neighboring note.

I'm not sure how you're using the term "natural seventh".

A C7#9 chord is not spelled "C-E-G-Bb-Eb". It is spelled "C-E-G-Bb-D#". 
Yes, a D# and an Eb are the same PITCH, but they are not the same NOTE. A technicality? Yes, but being technically correct can keep one from misunderstanding some things. A "C7#9" does not have a minor 3rd in it. It has a #9. (But you are right that the blues often makes an "ambiguous" use of the 3rd.) 

While one can technically call "C-Eb-E-F-F#-G-Bb-B" a scale. As you
describe it's use (assuming that you are playing it over a triadic harmony) is better understood as C mixolydian with passing notes added (Eb. F#, B).

By "natural 3rd" I assume you mean "major 3rd".

One fairly picky thing. I find the use of "legal" & "illegal" in a discussion of music theory distracting. (Who's "laws" are you referring to?)

Terry