Charlie of "Emergency Awesome" explains the history of the Faith Militant pretty well in this video:
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As for the names "High Septon" and their main building being named the "Great Sept of Baelor", just remember that the word "Sept" is rooted in the Latin word (Septem) for the number Seven, so yet more references to the "Faith of the Seven" in these names.

First cousin relations are accepted in Westeros, as they are in much of our own world. Tywin Lannister married his first cousin Joanna.

But she committed the crime of adultery. Tywin was not married to the king when he banged his cousin. Even if the king dies the queen is expected to stay true to him.