Those aren't real essays
That said, for papers like this, icu has the right idea. For generating ideas, I recommend jotting them down and doing some basic organizing before you start writing. I found that taking 10-20% of the writing time to brainstorm and organize helped immensely. You don't need to fully develop your main points before you start writing, but you should already have some support for them. More ideas will come to you as you write.
Since it's timed, you may want to find ways to speed up your writing. Try to avoid lengthy quotes. If your instructor will let you, citing by page and/or line number may be faster. Use active voice; it's shorter and more convincing. If your handwriting is legible enough, cursive is faster than printing.
Should I include how the passage affects the readers as part of the rhetorical strategies too? Would that take away from the focus, or add value to the essay?
I've had instructors on each side of this, so your best bet is to ask yours this. My opinion, though, is that your opinions of their effect belong in it.