Why is October 31 (or the Sunday before) celebrated as Reformation Day? I realize that's the day Martin Luther posted the 95 Theses, but there were other writings before and after that. When did the "Lutheran" Church as such come into existence with its own organizational structure separate from the Roman Catholic hierarchy?
Because the 95 Theses were translated, published and spread throughout Germany and other parts of Europe very quickly, and because the theses set in motion a chain of events involving the Roman Catholic Church and Martin Luther, the date of their posting is considered the beginning of the Lutheran Reformation.
Luther recognized he had no home in the Roman Catholic Church when the church excommunicated him in 1520. Lutheran churches began organizing in Germany as early as 1523. The organizational structure of Lutheran churches in Germany and elsewhere in Europe was not consistent, but Christian freedom allows such variety.
Northwestern Publishing House has many resources on the Reformation available. This link will take you to the appropriate section of their web site.