You say that Islam recognizes no 'chosen people'. How does the Koran justify this? Does it state that the coveneant w/ Abraham's children is broken? It it extended to others now?
The Israelite prophets are recognized, but prophethood and messengerhood were never limited to the Israelites or any single people. The covenant, according to the Qur'an, was bound to be broken by the "wrongdoers" among Abraham's ancestors:
And when his Lord tried Abraham with certain commands he fulfilled them. He said: Surely I will make thee a leader of men. (Abraham) said: And of my offspring? My covenant does not include the wrongdoers, said He. - 2:124
The annulment of the covenant is referred to repeatedly, especially in the earlier chapters. Specific misdeeds that led to its dissolution are described to some extent in the following passage:
And when We made a covenant with the Children of Israel: You shall serve none but Allah. And do good to (your) parents, and to the near of kin and to orphans and the needy, and speak good to men, and keep up prayer and pay the poor-rate. Then you turned back except a few of you, and you are averse.
And when We made a covenant with you: You shall not shed your blood, nor turn your people out of your cities; then you promised and you did bear witness.
Yet you it is who would slay your people and turn a party from among you out of their homes, backing each other up against them unlawfully and exceeding the limits. And if they should come to you as captives you would ransom them, whereas their turning out itself was unlawful for you. Do you then believe in a part of the Book and disbelieve in the other? What then is the reward of such among you as do this but disgrace in the life of this world, and on the day of Resurrection they shall be sent back to the most grievous chastisement. And Allah is not heedless of what you do. - 2:83-85
The universality of the institutions of prophethood and messengerhood are central to Islamic theology.
Surely We have sent thee with the Truth as a bearer of good news and a warner. And there is not a people but a warner has gone among them. - 35:24
And for every nation there is a messenger. So when their messenger comes, the matter is decided between them with justice, and they are not wronged. - 10:47
Muhammad's message, the Qur'an, was intended for the entire world due to his status as the "Seal of the Prophets."
Do you believe Aisha was the right 'leader' past Muhammed's death?
I believe that the only proper form of government under Islam is government by
shura, consultation, as mentioned in the 42nd sura. Aisha was certainly a remarkable and capable woman, but I believe that the concentration of power in a single person's hands should generally be avoided.
Why did your religion split so easily?
Disputes over succession. Shi'ites believe that Ali ibn Abi Talib was the rightful successor to Muhammad and do not believe that the first three caliphs (those who reigned before Ali) were legitimate. Moreover, they believe that caliphs should be of the family of Muhammad himself. Sunnis at least partially recognized the primacy of shura by affirming the legitimacy of those caliphs who were appointed by councils following Muhammad's death. I believe that they're both somewhat incorrect and that the shura councils themselves should hold political power.
does the Koran not establish any authority the way the Torah established the Jewsh councils? Is thre made no test to know a rightful Kalif?
As mentioned, Shi'ites believed that rightfulness could be determined by Muhammad's blessing and lineage while Sunnis believed that it could be determined by popular opinion and consensus. The only relevant Qur'anic passage is the following:
And those who respond to their Lord and keep up prayer, and whose affairs are (decided) by counsel among themselves, and who spend out of what We have given them; And those who, when great wrong afflicts them, defend themselves. - 42:38-39
Do Koran says that jesus was a Prophets, yes? How does it square this with his claims of divinity? Is it not the case that one who claims to be divine either is so or is a false prophet and a deceiver? How does the Koran actually address this?
The doctrine of scriptural corruption is also central to Islamic theology. Islam holds that most Jewish and Christian belief is based on misinterpretation or outright distortion of Biblical passages. The Qur'anic Jesus seems to be aware of this.
And when Allah will say: O Jesus, son of Mary, didst thou say to men, Take me and my mother for two gods besides Allah? He will say: Glory be to Thee! it was not for me to say what I had no right to. If I had said it, Thou wouldst indeed have known it. Thou knowest what is in my mind, and I know not what is in Thy mind. Surely Thou art the great Knower of the unseen. - 5:116
Why do Muslims call themselves Muslims and not Jews, if they believe in the books of the Jews and merely hold that two more prophets have come?
Qur'anic Islam views itself as a departure from the excesses of Christianity and Judaism at the time and a return to what it believes to be the strict monotheism of the prophets. The use of the Qur'an, the words of Muhammad, as its primary text makes Islam vastly different from Judaism.