What files are accessed when an app starts up?
I think there's a couple of options. You could use a launchd script with a WatchPaths property that triggers on those directories.

You can also use the command-line tool lsof to list open files of a process.

You can inspect open files per-process using Activity Monitor. If you click on the process and click "Inspect", it should bring up additional information. One of the tabs here should be for open files (see below).