Statesboro, GA, USA
A lot of questions there. There are two answers to the question of "why denominations" that I can see. One is positive, the other negative. One is the normal and even healthy expression of diversity. Though truth is exclusive in many ways, it is also living and organic, not brittle like frozen tin. Hence many denominational differences fall under that heading. The negative answer is pride and sectarianism, which is not content with being diverse, but wants to cut the dividing lines as deep as possible. Jesus Christ, and Paul both expressed warning against this tendency.
So there's a lot of good diversity that never would have found expression if the "scattering" of Christendom had never happened. But there is also much contentiousness and smug pride as well mixed in along the way. It's a phenomenon that we'll not fix by fiat or ecumenism, but which God has promised to deal with. Jesus spoke of there being "one fold".
I do recall C.S. Lewis commenting that while the world thinks Christianity is dying of old age, in reality our present divisions are more like the infantile pains of cutting teeth and colic. (He wasn't euphemizing the sin involved though, but rather speaking from a Heavenly view).
I think if we prayed for one another as much as we found reasons to separate, we would be much further along.
As to a discussion of the doctrinal variences between Roman Catholicism, Anglicanism, and Protestantism, I'll have to look into suggesting some reading for you. I would however encourage you to study (most importantly) what is their unifying reality (often in spite of themselves). "Mere Christianity" by C.S. Lewis is a great book to get you thinking in that direction. "Mere" meaning the basic and unadorned message of the Gospel.
Let me know if I can help you in any way.