You do not need to install any backend technology to work through the Flex in a Week series. Data retreival in the series is performed against a live server that is already set up; the appropriate details are in the exercise directions.
If in the future you do want to learn how to create the code for the backend, you can choose any technology that can be accessed via HTTPService, WebService or RemoteObject components. You will learn about these components in Days 2 and 3 of Flex in a Week.
Also, when you install the Flash Builder trial version, consider installing the Premium, rather than Standard Edition so that you can follow the steps for using the Network Monitor.
Also, regarding your question about an FAQ: There is a video listed at the top of the Flex in a Week page (http://www.adobe.com/devnet/flex/videotraining/) that is called "Watch a short overview video." This will orient you to the FiaW series.
If you have further questions about the series, you can post them to this forum, which is monitored.
I have just made my first application in Adobe flex without any backend.