5. Apart from the Jizyah and Kharaj, Are there any other obligations on non Muslims living in the Islamic state…?

Yes there are...
Both Muslims and non Muslims in the Islamic state are obliged to abide by the Islamic constitution since they are members of the Islamic state. This should not deprive them of their religious freedom which means: They are not required to fulfill any Islamic religious duties such as the Zakat (alms) or the Jihad (fighting).
They are not obliged, either in their personal or social affairs, to abstain from anything which is lawful in their religion even if it is not lawful in Islam such as consuming pork and wine.
Non Muslims Personal and social affairs are dealt with in their traditional courts or in the Islamic courts according to THEIR choise. The Holy Quran states:
“So if they come to you (O Muhammad), either judge between them, or turn away from them. If you turn away from them, they cannot hurt you in the least. And if you judge, judge with justice between them. Verily, Allah loves those who act justly.” (AlMaidah: 42)
This case has been applied throughout the Islamic history so clearly that no one dares denying it. Adam Mitz says: “Since the Islamic Shariah was intended for Muslims, the Islamic state let non-Muslims settle their disputes in their own courts. Bounded by the Shariah, the Islamic court did not interfere with the jurisdiction of these courts which adjudicated upon matrimony, succession and related issues among the Christians.”
This way of dealing with non Muslims disputes is still applied till now in Egypt where disputes concerning marriage and divorce among Egyptian Christians are settled by the Egyptian church, not the Egyptian courts, according to Christian rules.
Non Muslims however should abide by the Islamic constitution in cases of murder, wealth, honor, civil and criminal affairs, selling and so on just like the Muslims. In this case they have the same rights that Muslims have and the same obligation as on Muslims. Thus if a non-Muslim is found guilty of a certain charge, he would be punished exactly as a Muslim would if accused of the same charge for the non Muslim is supposed to abide to the Islamic constitution in matters which do not contradict with religion.
Non Muslims should live with the Muslims in a state of mutual respect to ensure peaceful co-existence in the Islamic state. Based on this rule both Muslims and non Muslims are not allowed to publicly abuse the others religious beliefs. Non Muslims are not allowed to openly indulge in the consumption of wine, pork or other items prohibited in Islam and they are not allowed to sell those prohibited items to Muslims (they can sell it to other non Muslims).