no, there is no relation at all
there is no separation between church and state
Between the two types of the Islamic religion it was the Sunni.
Its location between Europe, Asia, and Africa made it a center of trade between the continents.
The question is what can be called "mixing apples with oranges". The reason the question is poorly structured is that it asks the differences between a nation, the USA, and a religion, Islam. The USA has Islamic peoples, and Islamic peoples in Indonesia, the Middle East & Malaysia all have differences. There is no single "American religion" and there are no "Islamic" peoples that live in nations where Islam predominates that have the same cultures. In fact, in some European nations Islam is the predominate religion. Therefore there can be be no answer to this question.
Byzantine is anything pertaining to the Byzantium Empire or its period of existence. Islamic are those things relative to the religion of Islam.
Whomever came up with the Islamic religion came up with the differences between the 2 religions.
Yes. Between Islamic and Christian, between different Islamic factions (Shiite, Sunni, etc.), between fundamentalists and not-so-much-so. Members of the Baha'i Faith, the largest religious minority in Iran, are the most persecuted.
Carlos Slim Helu, the Mexican billionaire, was raised in a Maronite Catholic family. However, he is known to be private about his religious beliefs and practices.
Maybe the all of the dfferences come back to secularization and the relation between religion and world. In Islamic political philosophy, there is an emphasis on the role of religious authorities and on the succession of government according to Divine Laws and Religion. However, in Western political philosophy, since there is seculrization between religion and world, secularism becomes the foundation for these philosophies, albeit not all of them, but most of them, presupposing such a theme. In better words, the difference between them stems from the interference of religion in worldy affairs like government.
Haram is a prohibited activity in Islamic religion. A love bite is a way of expressing love and feelings between two individuals. Love bite is not considered haram in Islam, as long as it happens between a husband and wife.
The prophet Zoroaster was famous as being the founder of Zoroastrianism. It is considered the pre-Islamic religion between the centuries 18th and 6th BC.