I'm wondering if it is possible to jump to some specific app context or location based on the content of the live tile when it was clicked on. In other words, can some information be passed into the app on startup based on the state of the live tile?
If it's possible, an explanation or links to explanations would be swell!
You can pin Secondary Tiles that deep link into specific locations in your app. When the user launches your app from a Secondary Tile, your app will be passed the arguments that you set on the Tile when it was created. See Secondary Tile class constructor "arguments" argument. Once you receive the arguments, you can do with them in your app as you will (navigate to a specific location, for example). See this sample for more details.
As for navigating to a different area within the app depending on what's currently displayed in the live tile, that's not possible. The main tile will always launch the app to the default page, secondary tiles will always pass the arguments defined within the tile. There is no way to pass conditional arguments based on what content is shown. For example, there is no way to navigate to a different location based on which image in a series of images is being displayed.