When a society advances that generally means that we get more efficient, better at what we were already doing.
For instance, social media is us, attempting to connect with more people and be more social. 50 years ago, we sent out pictures of our families during the holidays, and we bragged on the card about what awards little Johnny had gotten this year, promotions, vacations, new cars. Now we can do that every day, as it happens on social media.
War, killing people is one of the things we do, we've just gotten more advanced. Before, back in caveman days we had to do it with our hands, or a rock. Eventually we got spears, then knives, then swords, arrows, guns, explosives, and finally, the a-bomb.
Now, cooperation is a part of what we do, but we've always been better at war.
Before I answer your question, I have to accept that the most advanced version of a human would be bad at war. War encompasses defense of one's home as well as offense.
I would have to accept that there's no evolutionary advantage as far as being good or predisposed to war.
I clicked on your link, having written this, and found this as far as Permalites are concerned:
The Pemalites were a highly advanced dog-like race who knew only of peace and playfulness. They were created by the Ellimist to counter the surge of killing from Crayak. When Crayak discovered the Pemalites, he sent the Howlers to destroy them. Because the Pemalites knew only peace, they had no way to fight back, which lead to their downfall.
Then it goes on to say that they are pretty much extinct because of this. There are two things I notice about the race.
1) They were created. Natural selection doesn't happen in their early development. It sure does later though, which is why this unwarlike race pretty much gets wiped out.
2) They "only knew of peace and playfulness." If that's the case, they didn't come from a warlike race which then advanced beyond war. They are not an example of that. Their creation implies that as well.
You had two questions: how would a society function that was beyond wars/competition? And how much advancement would humans have to do to move beyond wars and stuff?
First, as the Permalites show, by nearly dying out, and only surviving because they have a protector, being bad at war isn't an evolutionary advantage. If there are, indeed, others in the stars who would kill us, we would best have to know how to defend ourselves. That's part of war. The best example I have seen are the Nox from Stargate. Because they don't want to fight, they've learned how to hide and will simply remove weapons from aggressors.
Notice that they are so powerful that they don't have to fight. They have a choice.
The Nox live in the woods and have an internal life sense. That might be part of the reason why they don't fight--they draw energy from all life. It is to their advantage that they don't.
Humans have no such bio mechanism. However, in order for us to become a pacifist society, a few things would have to happen
- total change in cultural norms (all games would be cooperative)
- a real evolutionary advantage from peace (like drawing from living things as the Nox do in the example above)
- powerful enough that we simply banish all threats. If we are not, we will die like the Permalites OR we become totally dependant on another race that can protect us and wage war
More advanced does not necessarily equal more peaceful, so the second question you had on how advanced we would have to be, does not have a premise I agree with. However, do see the third point above "powerful enough that we simply banish all threats." That's tough to do, because there's always someone bigger...