The Church’s relation to the Trinity?

I recommend reading the Aidan Nichols, Epiphany: A Theological Introduction to Catholicism, 2nd ed. (Ex Fontibus Company, 2016) Epiphany, ch. 9: “The Rites of the Church. you might find most of the answers on chapter 9 of the book I mentioned above.
In essay form and in no more than 700 words, please upload a document defining the Church in terms of her source, nature, structure(s), and mission. In order to provide an adequate definition, you should at a minimum address the following questions:

(1) What is the Church’s relation to the Trinity?
(2) What is the Church’s relation to the Incarnation?
(3) Why is the Church both visible and invisible?
(4) Why is the Church hierarchical?
(5) Is the Church sinless? Why or why not?
(6) What is the purpose of the Church? Why does it exist?

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