Is there a way to move the Applications or Files & Folders buttons on the Unity Launcher? I can move every other button but those. I'd like to move them to the top of the bar instead of their default at the bottom of it.
Yes but they need to be within their group and files&folders and applications are 1 group. So you can put files&folders above or below applications. There are a few other launchers that are added to this group like the askubuntu (askububtu.place), google books (books.place) etc.
Basically we currently have 2 groups (hold the 'super' key while reading this and look at the launchers): digits and letters. And you can change the order of the group with digits and the group with letters.
Those digits and letters are inside all the *.place files on your system.
For instance /usr/share/unity/places has 3: applications.place books.place files.place
(Ofcourse changing the =a to =11 did not add applications to the other group so it will be something inside the Unity system the takes care of this...)