Do the harder settings make the AI cheat or anything like that?

I dont know exactly, but I've just completed the action pack on 'Hard' and from what I can tell the enemy firing rate is increased with the harder difficulty.

It has been some time since I played on medium, but I get the feeling the distance at which you are seen by the enemy is further on the harder difficulty.

While I haven't played around with the original on HARD, I have tried the second game, Saves are limited and the AI gets cheatsy (You can fire at one from a distance with a rifle, and if he's not dead, he'll whirl around and can instantly headshot you with an non-scoped rifle) I just play on Normal

No real cheats, but their accuracy, sensitivity, morale, and other parameters get considerable boost, i.e. "the firing rate went up" means up to the physical limits of the weapon, not like cheating over that and firing even faster.

Also the instant turn toward sound and spotting the attacker is still calculated with proper "vision" system (not fetching player position directly from memory, but the "vision" must see the player... the "vision" system is calculating line-of-sight from eyes of enemy towards various parts of body of other soldier, and if there are enough parts visible for the state "stealthiness", then the "suspicious" is reported and next level is "enemy spotted" ... on "hard" it's maybe 3-4 body parts checks away only, which can be under half a second, the visibility tests are gathering the data over period of time to not kill CPU with too many line-of-sight tests in single frame), if you are hidden enough, you may get undetected, although the firing sound + flash are like very strong beacons and it takes about second or so to "normalize" the visibility of your soldier back to the original state.

In some aspects the AI is on par with top human players (accuracy and firing rate), in other it's only AI (tactical/strategic planning), sometimes being mediocre, sometimes being completely random dumb.

I.e. on "hard" you better don't want to engage in "fair" fights, but instead outwit the enemy and eliminate them in the most unfair fights you can set up. Once you engage them in "fair" shooting fight, better be Quake-pro level player. :)

And IIRC, the spotted player position gets shared within the group of near-by AI instantly, i.e. once one AI does see you from the group of enemies, they are all instantly aware of you (it's like the "enemy spotted at" message is said between humans, but instantly and more accurately).