Is it correct that composers of most popular genres use 12 TET based interval consonance and dissonance when building chord progressions and a composition as a whole?
No, not really. I mean, it's true that popular songs use mostly 12 TET for their framework (although not strictly, since singers don't stick to religiously to 12TET, not do lead guitarists or many other instruments), but "interval consonant and dissonance" is only 1 part of composition, and isn't enough to define how and why chord progressions work. It is one part of the equation, but still only paints about 10% of the picture (to be completely unscientific for a second)
If you're talking about melody (i.e., horizontally), then the "consonance" of an interval used in a melodic step is not really relevant to making a good melody; melodies may move in half steps, whole steps, thirds, fourths, fifths; the consonance or dissonance of those stepwise movements when expressed as intervals is rarely a factor at all (unless outlining some implied harmony).
When talking vertically, unless you're talking about a melody played against a drone (like in Indian classical music, which doesn't use 12TET), then "interval consonance" is not going to tell you all that much, since music uses way more than 2 tones simultaneously.
So let's dispense with intervals and talk about chords (as you said in the opening to your question). The consonance and dissonance of specific chords is of course one of the factors in composition of a song, but it's by no means the only factor. Why some harmonic movements work isn't just a factor of consonance vs. dissonance, there are many, many other factors (otherwise C major to G major would sound the same as C major to Eb major; they're both a movement between 2 equally consonant chords).
If what you're looking to do is obtain a scientific measure of consonance vs dissonance then I believe that there are some equations that psychoacousticians have written to try and scientifically describe this human perception of frequency (links at the bottom). But measuring consonance and dissonance doesn't in itself explain either melody or harmony very well at all.
Let's be scientific, and take a premise (the one more or less implicit in your question): "consonance (as defined scientifically by frequency relationships, sometimes called "acoustic roughness") is the primary determiner of how chord progressions are determined in western music."
With that premise in mind, let's think scientifically. What would this model predict?
Well, take the following 3 chord progressions for example:
(1) | C | D | F | G | C
(2) | C6/9 | D9 | Dm11 | G13>G♭13 | CΔ9
(3) | CΔ | Am6 | FΔ7/A | Ab6/9 | C
You should expect them to sound radically different.
Why? In terms of consonant/dissonance relationships they're all over the shop, almost as far apart as you can guess. And to add to that, the movement of the roots is in different intervals too (if you want to look at it in a stepwise approach).
How do they actually behave though. Well, they're very close to each other; in fact they could all be used completely interchangeably in certain musical contexts (I've deliberately given extreme examples to stretch the point as far as possible, but it's still the case).
Now, for a converse example, let's look at the following chord progressions:
| C | D | F | G | C
| C | B♭ | G | F | C
| C | A | B | F♯ | C
You would expect them to sound and behave similarly according to the "consonance/dissonance is what's important". They're all combinations of major chords, and so with exactly the same "consonance". But 1 sounds like a basic chord progression, and 3 is almost completely unusable.
1 and 2 have the same interval steps between each chord, and yet they're still completely different beasts (way less similar than the chord progressions above for example).
So I think we can see from this that a model of harmony based only on "chordal consonance" is insufficient (in fact; useless) to explain (and therefore, conversely, to build) chord progressions and compositions as a whole. Chordal consonance is 1 ingredient in a vast array of (sometimes complimentary, sometimes competing) elements that make up melody and harmony. A significant one for sure, but not by any means a standalone "explainer". And, of course, melody and harmony are themselves only 2 elements that make up "music" as a whole.
Basically, consonance and dissonance exists, and is important, but is just one piece of a large large puzzle.
Now, that said, if you want the list of intervals by consonance as plain intervals (without musical context) it's conventionally (from memory):
Octave P5 P4 M6 M3 m3 m6 m7 M2 M7 m2 b5
That's in 12TET, and pretty much all other meantone temperaments too (of which 12TET can be considered a "special case".
In just intonation it's the same, so long as you're not using the 7:4 harmonic seventh, in which case m7 jumps up the pecking order a little. But conventionally the m7 in just intonation is represented by 16:9 (2 fourths) or 9:5 (p5 + m3). The same with tritones, if you consider just tritones then they can become a little more consonant, but that's quite a complex problem, so it's best to leave it out.
Of course, musical context changes this. A M7 can sound much more stable in a major 7th chord or a minor 9th chord for example than it does in a minor major 7th chord. Even a tritone can sound consonant in a spacious, airy voicing of some sort of lydian-y chord, like a good voicing of a Δ♯11
links for places to start looking about mathematical descriptions of consonance and dissonance.
a stack question about it:
Is there a way to measure the consonance or dissonance of a chord?