Please don't hold me to this, because a) it's been a while since I took the assessment, and b) I have a really really bad memory.
From what I remember, you have to take the entire assessment at one time. You can't take one part, save it and come back to it. It's timed (I think you get 3 hours), and the questions aren't all that difficult, so you should have time to...ahem "check" your answers. I'm glad that I went through some of the lessons and quizzes on the Khan Academy website. (Picturing Vin Diesel teaching Algebra II was enough to keep me going!) Definitely focus on Algebra I, II, as well as some Geometry. I also went to my local library and got a few books on the SAT. I focused not so much on what they were teaching, but the test-taking skills that they recommended. The first part is all multiple-guess and you can go back and change your answers before you submit them. Don't let test anxiety get you on this one. Seriously. You can do it in your favorite place, with your favorite person and/or pet sitting right next to you, with your favorite latte. Also remember, you don't have to score a perfect 100% so there is some wiggle room in case you accidentally pick the wrong answer. Three hours should be plenty.
For this test, you do not have to go to an exam center or have a camera on you, so you can absolutely use a calculator...or any other "resources". My understanding is that it's only after you've been accepted, and if you're in the undergraduate program that you take objective (multiple-guess) exams and thus you are proctored/watched. (Sorry to use that word for any guys reading this.) In my MBA (graduate) program, all of the exams are actually papers. There are no tests where I need to memorize things.
What took me the longest was the paper. I was all nervous and wanted to make a good first impression. If memory serves, it was a paper in which I was supposed to write about something where I had to overcome a significant obstacle in my life. (How deep!) I wanted to write about something deep and truly meaningful. (I wrote about finishing my first 100 mile running race. I figured I could use that to prove that I could overcome obstacles that might await me in school if I was willing to put myself through 100 miles in 36 hours.) The content is really not all that important. Your grammar and sentence structure seem to be the most important parts of the paper. Also, who says it has to be truthful? Heck, make something up. Write about something your cat overcame. I truly don't think it matters and I don't think any person actually every sees it.
I took the exam around 2AM. I seriously doubt that a person was sitting there waiting to grade my exam so the fact that my results came back before I could brush my teeth and get to bed (10 minutes or so) tells me that it was all computer-graded. If you can write coherent sentences (which from your email, you obviously can) that part should be pretty easy so don't stress. Focus more on the math portion.
Don't take the initial assessment lightly though since I believe that if you don't pass the first time, you have to wait a few months to re-take it.
I hope this helps! Good luck with the initial assessment. I believe in you!