Almost any writing involves collecting evidence, if you think of evidence as information gathered to develop or communicate an idea. Different writing tasks require different types of evidence, however.
In Essay I, the evidence will be your memories of writing when you were younger and (where possible) texts--essays, stories, letters, or poems that you wrote earlier in your life. This evidence will allow you to come up with idea about you as a writer.
In Essay II, the "evidence" will simply be your memories about a particular incident that relates to how you came to understand what it means to be a boy or a girl, a man or a woman. But they become evidence in the sense that, presented as they are in your story, they make an implicit argument for a particular we of understanding gender development.
In Essay III, the evidence will be the texts of the stories you and your classmates have written in Essay II, plus an other relevant observations of culture or behaviors related to gender development. You will look for patterns among the stories to come up with an idea about gender development in boys and girls.
In Essay IV, the evidence will be derived from your response to one author's perspective on a gender issue; thus the evidence will be both your close reading of an author's text and the author's text itself. All this evidence will allow you to write a review of an essay on a gender issue of interest to you.
Finally, in Essay V, the evidence will be everything you've pulled together--memories, observations, student texts, published texts, and close readings--to articulate a position on a gender issue of interest to you.