"First of all, I don't think that DEET will dissolve in water, so forget that."
It's true that it doesn't dissolve in water, but it can still be diluted with water immediately before you apply it. It forms an emulsion, not a solution, but that doesn't matter. The motivation for diluting it is that you get more mileage from the same pack-weight of 100% DEET. The down-side is that it has to be applied more frequently. To me, the convenience of not having to re-apply it all day outweighs the slight reduction in pack weight. People who use the technique typically squeeze a little deet into their palm, add some water, mix with a finger, and then apply it. Some people use a fold-top baggie instead of their palm.
Personally, what I do is to squeeze a drop of 100% DEET on the back of my hand, then use the back of my hand to rub it on the area where I'm applying it. All I normally apply it to is my head and the backs of my hands, and that only takes maybe four or six drops.
"I just did some investigating out on the web as to how DEET works. The consensus is that it blocks receptors on the female mosquito's antennnae that detect CO2 and lactic acid, two compounds that your body produces which the mosquito uses to home in on you. Apparently no one knows for sure how it works for all insects that it repels, or even all mosquitos. Research is ongoing."
How old are your sources of information? This 2008 paper contradicts what you're saying: http://entomology.ucdavis.edu/news/DEETresearch.html , Zainulabeuddin Syed and Walter S. Leal, "Mosquitoes smell and avoid the insect repellent DEET," PNAS.org
DEET dissolves polystyrene, ABS resin, styrofoam, most synthetic fabrics, and polycarbonate. This includes bear canisters and the materials used in a lot of steering wheels.
It won't harm nylon, silnylon, or polyethylene plastics.