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1: How does one MOD the AI files?
You open them in text files and start playing with the values in there.
I don't know too much about AI modding, but others do.
2: How do ministers work and how can they be utilized well?
They will control parts of your empire for you, using the AI. But, they are not very good, and it is generally better to control your empire yourself.
3: Is it possible to MOD colony modules to only colonize specific atmospheres?
No, it is not.
4: Can Argon be used as an atmosphere type?
You can not add any new atmospheres.
5: What is a good place to get free web hosting from?
http://www.spaceports.com
6: Does anyone think it reasonable to have both regular armor and shields and the "leaky" variety (smaller and cheaper) in the same MOD?
It depends on how it is done. You can make the regular armor only have about 1/2 or fewer hitpoints as the leaky armor. But, combining normal and leaky shields gets very tricky, and probably shouldn't be done.
7: What are the weapon and component family fields for?
They determine what an item will be made obselete by, and what will be replaced by what when you "Upgrade" a design.
8: What (or where can I find out which) abilities can be used with what items (component, vehicle size, facility)?
Look in Abilities.txt. It lists a few. Check out my SE4 Modding 101 tutorial, linked in my sig, for some more pointers.
9: What happens if an ability is used with an illegal item?
Nothing. It will list the description of the ability in-game, but it will not funciton (that ability, at any rate).