On Windows 7, is there any way to track what a specific application does on my hard drive? (like what files it accesses, creates, edits, etc.)
You mentioned "exe" so I assume you are on Windows. Try Process Monitor.
If this is a windows machine, I highly recommend using process explorer directly from Microsoft (process explorer - microsoft.com). This will give you all the information on any process running on the computer, as for all dll files and what not touched or opened by that same process.
By the way guys, I sent him to the Microsoft page where all the sys-internals tools are all located... grawity...