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I don't even know why you should be worried with sound insulation apart from the typical separation between the CR and the TR since it seems you are in the middle of nowhere !

What you should be wo ...

my greatest advise... don't dry the room and use some diffusion

I know closed cell foam but they don't absorb much energy. One of the foams is called Quash

An acoustical engineer can make a room sounding good, either if he chooses to splay the walls or not. There are advantages and disadvantages on both situations. This is a matter of preference of the e ...

I agree with avare.. For weird rooms you can use FEM, I just did that once and find it to be a bit time-consuming.

Musical acoustics is another option you should look at.

You can use the wave equation to find mode ressonances, shapes, etc etc...

Get the book Room Acoustics by Kuttruff. This is a great starting point in terms of math. This is not a book for small roo ...

Non-parallel walls cut down on the ping-pong effect from direct reflections and helps minimize standing waves.

Non-parallels walls shift standing waves but they still exist. Newell's book has a ni ...

http://www.sound-map.com/images/1110002391/04.jpg

Here's a picture !

Of course, but you are supposing a loudspeaker radiates sound with the same directionally where in fact it does not at medium and high frequencies. So in terms of pure mathematics it seems the same bu ...

The methods I know of predicting TL are a bit empirical. Search for Ben Sharp or Messneir. A book which has some info is Engineering Noise Control by Bies and Hansen. But only related to double walls ...

Non-Parallel walls are useful to create a Reflection Free Zone but they are not mandatory. You can build a professional studio with parallel walls (of course by having proper acoustical treatment).
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The concepts of soundproofing a room are the same be it preventing the sound from coming in or out.

Low frequency soundproofing means double walls with big air cavities. Soundproofing vibrations is ...

Those NRC values from carpet are ridiculous for such application in a theater. Perforated panels have at least the double of the NRC.

One thing I know for sure.... I'm not sure you can use carpet in a theater unless it is fire-rated.

Second thing I know.... carpet absorbs medium and high frequencies and you already have absorpti ...

Is this a real theater ? A public space ? Ain't that acoustical fire rated, what you meant ?!?