Tapegum is a dedicated paste consistency stuff to caulk between drywall gaps, and it is very elastic, in fact it never becomes solid, and also hydro-insulator.
Sounds perfect! That should work well. Just leave a slight gap between the drywall panels as you put them up, maybe 2 or 3 mm or so, and force that tapegum stuff well down into the gap, to make sure you get a good seal. If you have long walls, you might need to adjust the framing so that the drywall is still centered on the studs: EG. 6 panels of drywall next to each other with an extra 4mm gap for each is 24mm, so that's off the edge of the stud!
The additional frame is present only in the gap between the windows, and will sustain the drywall I will use to seal inner space between the windows from the gap between the walls.
Don't seal that with drywall! That will connect your inner leaf to your outer leaf, defeating the decoupling. Just use Homasote board, add a piece of OC-703 insulation on top, then wrap that all in black fabric. Glue that to ONE side of the gap (probably the brick wall side), and let it float just a bit above the other side, without touching (or touching only very lightly).
I used REW's sound generator through an active monitor, and measured the sound level inside and outside the studio with a professional handheld decibel-meter.
Ahhhh! OK, then that's fine: You were just using it as a tone generator. When you mentioned waterfall plots, I though you were trying to measure the transmission loss through the walls with waterfall plots!
I had surprising answers from two sound treatment companies ( I am not sure if I can write the names so I won't) - using their free room evaluation:
They went there to your place for FREE, and evaluated your room with proper test equipment? At not cost?

If not, then I would not trust their assessment very much! If this is one of those services where they say "E-mail us your room dimensions and we will tell you which of you wonderful kits you need to buy", then be VERY aware... that's not a good way of determining what treatment your room needs.
This is something that you CAN measure yourself with REW, then post the data files here.
because I got the measurements right, and have no parallel surfaces nor 90 degree corners.
Ummmm... well.....

I would not trust what they said at all then! Good room measurement do NOT make room modes go away: they just spread the room modes a bit more evenly. Making the walls non-parallel does NOT eliminate modes: In fact, it multiplies them. Sure, the axial modes might get a bit weaker, but you have to angle the walls quite a bit before they disappear.... and at the same time, you are creating many new tangential and oblique modes, which replace the axial modes....
Also, by angling your walls you make it impossible to predict the modal behavior using simple room-mode calculators, and then the only method for doing that is by using expensive FEM/FEA software, and paying a good operator who knows what he is doing to set up the boundary conditions that simulate your room, and then interpret the results for you... I guarantee that the "free analysis" people did NOT do that, because it costs money. So if they knew that your room has no parallel walls, and they still told you that you have good modal response, and they did not actually go to your room and measure it acoustically, then sorry, but they were rather less than honest with you.
Here's what you should do to find out for sure what the modal response of your room is, using REW:
Place your speaker down on the floor in one corner of the room, right in the corner where the two walls meet the floor, with the speaker facing down the length of the room (the longest distance, not the shortest distance). Now place your measurement mic up in the exact opposite corner of the room, where the other two walls meet the ceiling. Point the mic right into the corner, as close as you can get it without it touching the walls or the ceiling. In other words, you have the mic and the speaker as far apart as it is physically possible to place them in that room, in digonally opposite corners.
Now run REW, and post the resulting MDAT file here on the forum. It might be too big to post here, and in that case use a file sharing service such as Dropbox, and post the link here.
Then I'll download that and analyze it for you.
This is what REW is designed for: to measure room response. It is very good at doing this, and will certainly show the real modal behavior of your room. The reason for putting the mic and speaker in the corners, is because all room modes terminate in the corners, so by using the "tri-corners" of the room, you are triggering all possible modes, even down to the lowest frequencies, and also measuring them at the best point.
In fact one of them said that I don't have any axial mode problem,

We'll see if that is true or not...

REW doesn't lie, and REW doesn't want to sell you a kit made up of pieces of foam....
and the tangential ones are 2-6dB only,
That makes no sense: 2-6 dB ... with respect to WHAT?

Theory says that tangential modes will be 3 dB lower than axial modes, and oblique modes will be 3 dB lower than tangentials. But that doesn't mean much: that is only the maximum INTENSITY of the mode. What is important about modes is not so much the maximum intensity but rather the decay: How long do they carry on ringing? Do they decay at the same frequency, or do the change to other frequencies? Does the decay rate change, or is it constant? That's what matters.
but we will see after I will be ready.
It's better to see
now, so you can be prepared for the treatment in advance...
I guess, I will need yet some help.
No problem! That's what the forum is here for.... To help.
No idea of acoustics. As a read more, I am more and more convinced that I do not know jack about it.
Well, for somebody who doesn't know much, you seem to be doing a lot of things RIGHT! And it seems to be working out pretty well, so far!!!
- Stuart -