Iztok, one question related to this: what particular precautions do you take to prevent the other AI's from finishing you off once you've won the first war?
On Challenging or higher levels I usually have problems avoiding that; my research doesn't continue fast during that war because I need more focus on military production + after the war my remaining fleet usually just can't compare to the remaining AI's. Or it is comparable but then I get 2 AI's on my back who I can't bribe.
Just wondering how you go about it at those extreme difficulties
Challenging? I think you mean higher levels. Today, I won my Terran game on Challenging. Conquering other races has never resulted in the remaining races attacking me, I never had to stop research for military production, never lost a ship, and never got out-teched. My first war with the 1-planet Thalans was a cakewalk, and minor races didn't put up what could be called a resistance. Only the Drengin and Yor fought prolonged wars against me because they had tough soldiers, and were either on the other side of the galaxy(Drengin) or had Super Isolationist(Yor).
All the remaining races got Close after the fall of the Yor, I formed Alliances, and abruptly won a Diplomacy Victory with the Torians nearly outscoring me. I'll continue the game from the last save and aim for Technology Victory(which will take several more years).
I don't know about higher levels or lower levels though, or games with many planets. Maybe the AI works better when they have more than 2 planets(the norm in my Rare-planet games). Otherwise, when due to events or war, if the Bright-level AI gets stuck with only one planet, they usually become largely inept.