Galaxy Note 3 - Is there a way to add more apps to use when drawing a 'Pen Window'? Is there a way to add more applications in the list that appears when you press the button on the S-Pen and select "Pen Window" to draw a floating application?

It would be really nice if you could open a floating twitter or Facebook application.
Without root it is up to the developer of the particular application, and chances are there aren't enough Note 3s out there to justify it.
There is an S-Pen SDK from Samsung
There are lists (but these will often be out of date in no time)  like this best S-Pen apps out there.

With root access  there is a way to open any app in Pen Window Mode

First, make sure you are rooted with busybox installed.
Second, make a backup.
Third, just download PenWindowManager_v1.apk  and install as normal.
Finally, just tick the apps you want and don't forget to press the save button. A soft reboot maybe required for the changes to take effect.