I'm looking to mount a cheap 7" android on my wall to display current tasks, events and household requirements. Does android 4.2 have a built-in tool that can download a file from a server every 5 minutes and display it on screen? I know it must have rsync but I'm not sure about the displaying information
There's no built-in tool to do this - why would there be? - but there are several apps available depending on exactly what kind of information you want to show and how you want it displayed. For example, you could do worse than my app Showr, which is a home screen widget. You tell it the web address of an image file, or an RSS feed with images, and how often to update it, and it updates the image and displays it on your home screen. It's a free download from Google Play. My users often use it to display information like weather maps and charts, as well as more fun things like webcams, photo blogs, and logos or pictures of things or people they like.
You might also use home screen widgets for other kinds of information. For example, if the events you want to display are in a Google calendar (or can be imported into it from an iCal file or similar), then the Google calendar app can display upcoming events in a list on the home screen.
There's quite a few task list apps too, and they usually have home screen widgets and push capabilities, so if you add or complete a task from your phone, the list on the wall updates automatically. Remember the Milk is one such, which I use, but you have to pay a subscription for unlimited syncing.