Why did the Uchiha Clan want to Rebel?

1. Itachi is not an evil guy, he is a double agent. He does the killing for Konoha because the entire Uchiha clan was planning for a coup de'tat against the village and Itachi, who already have seen so much slaughter in the ninja war, does not want more blood spilled, so he kills everyone in the clan including his parents. The third Hokage was against the policy from the start and the killing took place without his permission. It was headed by Konoha elders, Danzo and ANBU under him.

2. Why didn't he kill Sasuke? Because he loved his brother and he couldn't kill him. He wants Sasuke to be an Avenger so he can become powerful and, because of his hatred for his brother, Sasuke can surpass Itachi. Finally Itachi plans their final battle so that by the time he dies he transfers his eye techniques. Yes, Sasuke gets the Mangekyo after that showdown and Yes, Itachi dies at the end of the battle.

3. How does Sasuke know about this ? It's revealed to him by the Head of Akatsuki (Remember Itachi and Kisame were going after Naruto) which is a terrorist organization for which Itachi was a part of. He joined the group to keep tabs on the organization and secretly keep his eyes on their plans with respect to the village. the reason he comes to the village when he fights Sasuke is because he wanted to threaten Danzo to prove to him that he is alive so he doesn't cause any concern to Sasuke.

Konoha is one among the major five Countries and throughout the series the crux of the matter is being a Ninja is about making sacrifices and how much one pushes themselves for the sake of the mission and their Village. Itachi loved Konoha. To him the village meant something more than his clan, except his brother.

I hope I have clarified your question. if you require further clarification. Add a comment. I will try to explain furthermore.

Why did [the Uchiha clan] want to rebel?

The Uchiha Clan rebelled because of the many unfavorable conditions that the Konoha village leadership put on their clan, contributing to the mutual distrust between the two factions.

The Konoha leadership, starting from Tobirama, the second Hokage, had distrusted the Uchiha clan, and they grew to distrust each other more as time passed.

As per Itachi Shinden, after the Third Shinobi World War, no one from the Uchiha Clan was nominated to be a Hokage, despite their contributions in the war. And after the Nine-Tails' attack on Konoha, they were suspected to be what actually caused it (as the Sharingan is known to be able to control the Nine-Tails as, Madara did).

After the Nine-Tails' attack, the Konoha Police headquarters (which sustained heavy damage) and the Uchiha Clan houses were ordered moved to the outskirts of the village, too far from the village center, despite Fugaku Uchiha's protest. (Fugaku is the head of the Uchiha Clan, and Itachi and Sasuke's father.) The location can also be easily spied upon from several vantage points, adding to feelings of distrust between the Uchiha Clan and the Konoha Council, culminating at the Uchiha Clan massacre.

Third hokage doesn't seem to be the kind condoning genocide. Does this make Konoha a socialist country?

I'm not sure why you connected socialism to the third Hokage condoning or not condoning genocide. About the third Hokage, it was not his order to assassinate nearly all of the Uchiha Clan, but Danzo Shimura's, one of the elders of Konoha. The third Hokage was in favor of resolving the situation diplomatically.

Konoha is part of the Land of Fire (a country), which is led by a Daimyo. This is similar to Feudal Japan's form of government.

As to their supposed weakness, Itachi was an exceptionally talented Shinobi. Due to his back story, he was able to unlock exceptionally strong and rare visual jutsu.

He was inducted into the elite group of secret police Anbu at a young age. The group specializes in tracking down high level ninjitsu users and assassinating them. They use covert methods of "traditional" ninjas, attacking and killing while keeping concealed, while most other Shinobi attack loudly and in plain sight.

The Uchiha as a group are strong, and their clan has access to strong fire and visual jutsu. They rival the other clan enough that they were considered a threat. It would have been a civil war for the Leaf. Individuals vary in strength like any group but working together to attack they would be deadly.

Itachi was only able to kill them all through hypnotizing them at night, when their defenses were down and not expecting their clan member to attack.

It was a surprise assassination, done one or a few at a time by likely the strongest of the Uchiha.