This is a very interesting question. My first thought was that the mylar might melt when boiled, but in fact mylar is a type of polyester, so that should not be a problem; the melting point is 254°C (489°F). Since mylar is polyester film, it should take the dye about the same as the polyester lace overlay. I think that it will retain its metallic sheen, though to a duller extend since sone wavelengths of light will now be absorbed by the dye, so not as much light will be reflecting back at you.

Unfortunately, what we've observed in many cases is that a premixed dye color, containing two or more dyes of different colors, will produce a different hue on one fiber than another. This is because one of the colors in a mixture may work better on one fiber, while another works better on the other fiber, creating an imbalance in color. Just as silk produces a different color than cotton does when colored with the same dye, under the same conditions, we can expect acetate to produce a different color than polyester does; for example, if you use a turquoise dye mixture, it might come out green on the acetate, or the other way around. The only way to be sure that different fibers will produce pretty much the same hue is to use an unmixed, single-hue dye. This may or may not be available in the color you want, but since there are several possibilities, you'll probably be able to find one you like. With an unmixed single-hue dye, one fiber may take the color more or less intensely than another fiber does, but the hue will be a reasonably close match.

Some dye suppliers refuse to let you know what the dyes they sell are, keeping the Colour Index generic names for each dye a secret. One of the many things we like about PRO Chemical & Dye is that they are willing to share this information. The disperse dyes that have a Colour Index name are single-hue unmixed colors, and therefore the most likely to be suitable for dyeing your different fibers. You can see a list of PROsperse Disperse Dyes on my page about disperse dyes, but I recommend that you then also call ProChem and ask them specifically whether the dye you have in mind is a mixture. This is because, over time, sometimes a pure dye color becomes unavailable from the manufacturers, so that retailers such as ProChem are forced to replace them with approximations mixed in-house from other dye colors. It's always best to call to make sure that this has not been the case for the dye you have in mind.

Another issue is whether the different fabrics in the dress are starting out the same color. Since dye is transparent, the ultimate color will include whatever the original color was. Chances are that the different colors on one dress will continue to blend well after they have been overdyed, but it may be difficult to predict exactly what colors you will see.

Also,
(4)will natural cotton fiber or synthetic nylon take the PROsperse dye?  If so, I thought I might throw in a few random small items with the dress.

Nylon will take disperse dye, but cotton will not. The disperse dye may stain the cotton, but it should be mostly gone after a couple of washings. It will, however, dye the thread at the seams, since most cotton garments are sewn together with polyester thread. I recommend that you attempt to dye only materials made of synthetic fibers with your ProSperse disperse dye, including nylon, polyester, acetate, and acrylic.

I'd love to see you try this, because I'm very interested in what the mylar will do when you dye it, and whether or not my predictions hold true. However, I must point out that the most difficult pat of this procedure will be the boiling. You absolutely cannot use disperse dyes in the washing machine, because temperatures below a full boil will not work with disperse dye. You will need to have a very large non-aluminum cooking pot, large enough that your dress can move freely as you boil it with the dye. For a smooth solid color, you will need to stir the dyebath frequently. If the pot is too small, or if you do not stir frequently enough, or if there is any invisible substance that is on only part of the dress, then you will end up with a splotchy or even tie-dyed look, which is good if that's what you're going for, but very disappointing if you really want a single smooth solid color. 

Disperse dyes work best on polyester when used with a somewhat toxic carrier chemical, the Dye Carrier NSC, which is reported to have an unpleasant smell, and it is important to have good ventilation as you use it, with fans in fully-open windows blowing outward and a fan in another fully-open window blowing inward. You can use disperse dye by boiling it without the carrier chemical, but the color produced on polyester will be significantly lighter. Both nylon and acetate will take disperse dyes well without the carrier chemical, so they are likely to produce darker colors than the polyester will, though the hue should be a close enough match for the different colors to look good together.

Please examine ProChem's direction for dyeing with their disperse dyes, to make sure that you are ready to do it right. You will need to have another large cooking pot ready with water heated to 180°F in order to rinse the the Dye Carrier NSC from the fabric immediately after you finish the dyeing part of the process.

If you do dye your dress, please let me know how it goes! I hope that your dress is not too fragile for  the rather rigorous treatment required in order to dye polyester. 

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