For the essay section of the SAT, what is the last part you should write?
Your introduction and thesis statement. In a very short timed writing session like this, the best use of your time is to very briefly brainstorm a strongly positioned answer to the posed question, and then write the bulk of your answer, continuing to draw conclusions and make points about the topic at hand as you write. Lastly, after all of your major thoughts are down on paper, use the strongest points and explanations you have produced to compose a concise thesis and a compelling introduction. I have always found that saving the "hook" and thesis statement for last is best because you have had the fullest possible amount of time to think through a strong position and to work through the different aspects of the question at hand.
On the reading SAT section, should you read the reading passage or its specified questions first?
Glance over the questions first. There is no need to read through every multiple choice answer yet, but definitely read the questions about the passage beforehand to get an idea of what kinds of details to be looking for in the passage. Then, read over the passage carefully, answer the questions to the best of your ability upon one reading, and go back through the passage to search for the answers to any questions that remain unclear.
What is the most important part of a paper, essay, or any written response, and why?
The thesis. Regardless of what kind of writing you are completing, the thesis statement is the most important piece of any paper. This statement should concisely and completely encompass the ideas you wish to express and argue throughout your piece. Even if a paper is not explicitly supposed to be thesis-driven, composing a well-thought-out and eloquent summary of your piece's ideas will significantly improve the effectiveness of your piece, and will even help to shape the focus and structure of your piece as a whole.