Normally the shortcut created when the game is installed is to an intermediate "launcher" program. The problem is that cheat mode cannot be applied to the launcher. You have to create a new shortcut directly to the game executable and add the word "cheat" after that.
The best source for GalCiv2 info is the Wiki at https://www.galciv.wikia.com/wiki/Galactic_Civilizations_Wiki.
From the GalCiv2 Wiki article https://www.galciv.wikia.com/wiki/Cheats_and_keyboard_shortcuts
For DL use: "C:\Program Files\Stardock\TotalGaming\GalCiv2\galciv2.exe" cheat
For DA use: "C:\Program Files\Stardock\TotalGaming\GalCiv2\DarkAvatar\GC2DarkAvatar.exe" cheat
For TA use: "C:\Program Files\Stardock\TotalGaming\GalCiv2\Twilight\GC2TwilightOfTheArnor.exe" cheat
Of course the full path will depend on where you first installed the game. Ctrl-U eliminates the fog of war and the article lists a bunch of other options.
As far as how the AI does stuff the answer is that the AI does in fact *mostly* play by the same rules as the human. There are a few differences. One is that every time you load the game the AI gets a "production" turn. So if you loaded, saved and reloaded the AI could possibly have already rush bought 2 building on their home planet whereas you could only have built one. This is actually pretty minor. The more major thing is that the AI does know where the good stuff (resources and planets) are. Again this may seem like a big deal but in practice it's really not all that big. As long as you start as a race with stellar cartography you can tell where the stars are and how many planets they have from the mini-map. You don't know the PQ of the planets or whether they are immediately colonizable (DA or TA) but if you blindly send a colony ship more times than not there's something there for the colony ship to land on and if not there then the next system over probably will.
The key thing is the AI level that you're playing against. IIRC Tough is pretty much the "fair" level to play against and can in fact be pretty tough. At that level the AI plays to it's full capabilities but does not get extra resources. Below tough the human actually gets extra bonuses and above tough the AI gets extra bonuses.
The thing is that you will get used to a level and what seems impossible now will seem easy later, so start out where you're reasonably comfortable and when you master that level then crank it up a level. But watch out for that last step. The jump from Obscene to Suicidal is pretty huge.
