You can store patches top any User preset folder - not the other folders. But yes, you can go any of the other folders, edit the patch or not, and then save it using the described method to any User location.

The purpose of the other icons (arrow, 1+2, and the lock) are very clearly described, along with diagrams that I can't produce here, in the X3 User Guide on pages 4.7 through 4.10. Please read these pages again. Basically, the arrow and the numbers are used to select whether you want to recall Tone 1, Tone 2, or both when recalling a preset from one of the folders. The lock icon controls the Lock Tone 2 feature.

Here is the manual:

http://line6.com/data/6/0a060b316ac34f0593c1b466f/application/pdf/POD%20X3%20Advanced%20Guide%20-%20English%20(%20Rev%20E%20).pdf