To answer your biggest question:
The link you provided to a program called Cheese.jar is simply LateralGM (the IDE) paired with a plugin that simply attaches the game data to Game Maker's runner data, producing a bona-fide GM executable. It is still interpreted, and it is still windows-only. It also discards any GM7 or GM8 specific resources/data, and fails if you try to use any GM7 or GM8 specific code.
ENIGMA compiles your game to C++, which makes it cross platform and non-interpreted, along with the hundred other things that set ENIGMA apart from GM. The reason they appear the same is because they both use the same IDE, LateralGM. The difference is what goes on behind the scenes, when you press the Compile button.
a) It takes a long time (at least the first time) because it's not just slapping game data onto the end of runner data to be interpeted later. Your game is actually being compiled into machine readable byte code. Even the "runner" of your code, or the core code behind everything that happens, needs to be compiled the first time. However, after you've compiled the first time, the second and later times will all be relatively quick, since they only need to recompile whatever you've changed. This is also explained on our
Install wiki page.
b) I'm working on it. It will be available soon.
c) Ok, find me one. I've tried over and over again, and haven't found one.
d) Yes, almost any, but some features aren't supported yet. Yes, depending on what you mean by "safe", I can assure you that they won't be decompiled any time in the near future. Yes.
As for your offer:
You must be able to work with Scalable Vector Graphics (svg), and you must be willing to license them in a libre license such as the GNU GPL. All of our Drag and Drop icons were created by Quadduc, one of our team mates (who isn't active on the project anymore). Most of us found them to be not only suitable, but better than anything any of us could have done. As for the resource icons, we're currently in the process of replacing them with this set:
http://dl.dropbox.com/u/1052740/enigma/graphics/resources.svg . If you think you can provide a better set of icons, either DND, resource, or both, following my two criteria (svg and libre) then feel free to show us some, and we'll review them and, if satisfactory, apply them.