Does the AI "Cheat?"
Having played endless hours of Total Annihilation in various skirmish maps and some limited trips through the campaigns of the original TA 3.1 and then some extra work in the Escalation expansion, (I guess you could say I'm a bit of a purist?) I think I can answer your question.
Does the AI "cheat" (by giving itself additional resources, etc.)? If yes, what cheats does it do, and at what difficulty level(s) does it cheat?
What The AI Doesn't Do
The short answer is no, it doesn't cheat. It does not to my knowledge give itself any additional resources than what you specify in the skirmish setup screen.
If you had the ability to perform billions of calculations per second like most computers do, the computer would need to cheat because it would find itself matched with you at every turn and unable to beat you.
What The AI Does Do
The long answer is that while it doesn't give itself additional res, as the difficulty goes up, it does speed up or decrease the delay between the time it takes between finishing one task and taking up a new task. So an AI commander may take X number of cycles at Medium difficulty, it will take only
X * 40% of a delay on hard and yet
X * 150% of a delay on easy. This will have a direct impact on the AI's ability to wage war on you and your friends or enemies.
Likewise, the AI will limit it's use of certain tech or attack options. An AI under Easy will not usually build a Bertha/Intimidator. Under Medium, it will build one but it won't build it as fast or extensively as it would under a Hard difficulty level. Notice, for example that the out-of-the-box AI will never launch a nuke, even if they devote the resources to build several launchers. (Not true with your friends!)
Using a cheat code to take a peak
On a side note, typing in a cheat code
+control 0, where
0 is the number of the player (starting with 0) in the player list at the start, will allow you to take over that particular player in your skirmish. You will see all their units and be able to control what they are doing. The AI will still try to control it's creation, but you will see everything it sees.
Meanwhile, your own player controls will be vacant and without any new direction, so don't stay there too long! To get back to your controls, merely type
+control 0 which is your number if you started the game with you at the top of the player list.
This little peek should reassure you that the AI is not cheating or stealing resources.