When I power off the iPod, and restart it, does it re-open all previously open applications?
These applications are not necessary "running".  The multi-tasking tray doubles as a "recently used" list.   So although you may not have run these applications in the past week, they are listed in the order they last ran (however long ago that was).

So, to answer your question, no the iPod doesn't restart all previously open applications.