How to split a PDF in 2-page spreads into single pages?

Apart from doing it manually, as explained by @gary_sc , you can also do it using a script, such as this (paid-for) tool I've developed that will allow you to do it with a single click:

http://try67.blogspot.com/2009/09/split-pages-in-2-parts-and-combine-to.html

To answer your 2nd question, Split is for taking a 200-page PDF and converting it into two 100-PDFs

To answer your question is probably a tad more complicated than you'd like, but here it is:

To split a document, click on the Edit option. Under Modify Page, you'll see the Crop Page option.

With your document open, click on Crop Page and then Marquee one half of the page. I'll let you be carefull and determine how wide you need to be (I wasn't careful). When you're happy, click "Done."

After you've done the first page, you can see below that that is now a self-standing page. Note the right half is now gone. So, basically, you'll crop out the left half of the double pages, then take the original document and crop out the right half.

Then, merge the left half and right half together. Then, in Organize pages, you can reorder them in the correct order. You can then edit the text and renumber them as needed.

You are lucky that this is a short document. 

Good luck!