The AI does not cheat, and cannot see into the fog of war.
1. I had noticed that, because when I played against 7 comps at the highest level of A.I., and with the fog of war totally removed, I could see that my 7 adversaries started with the same number of ships and did not grow at an abnormal, excessive pace. I like that.
2. Consequently, my future games will have the fog of war totally on for myself. If it is turned off, it does grant me a very unfair advantage : I can see the ship strength of every planet on the map, and since I can perceive incoming attack trajectories, I can too easily prepare myself.
On Wednesday, I played 3 games (random/huge, max. planets, 7 enemies), on average, high & highest, and I won too easily : certainly, in a major part, because of my very unfair no-fog-of-war advantage. I'm certain that I will always win again, because I stockpile ships until I have a big enough armada to overwhelm my neighbours, and a big enough factory-upgrade level to generate a sufficient defensive force per turn (to secure my planet when my offensive armada has left). Since the A.I. don't seem to build enough factories, it won't be able to compete, in the long run. Not having the fog of war turned on will only make me more cautious & patient, but it won't change my factory building and ship stockpiling Strategy.
I prefer to play on vast maps, but I guess that the smaller the map, with the most enemies, the more the probability that very stressful, early threats can increase. I will eventually try that.