I am not able to reproduce all your observations. Assuming you deleted the CFSM folder in 'My Document', then CFSM loads songs according to how they are ordered/stored in the 'dlc' folder (mine are ordered by file name). The songs are not sorted initially on any column and no sort glyph (arrow) will be shown if you are starting with a 'clean install'. If you see a sort arrow then you do not have a 'clean install'.
The sort arrow will appear after you have selected a column to sort on. The sort arrow is only visible if the column is wide enough to show the sort arrow. If the column is too narrow then the sort arrow is not (can not be) shown. You can widen columns to see the sort arrow if need.
'Sorting Resets, Sorting Arrow is no longer in any column.' Sorting does not reset. The sorting glyph does become invisible. This seems to be a limitation of VS which may be caused by CFSM custom filtering method. I am unaware of a fix for this now known limitation.
'If I Filter items, I can move around without problems. When I Click a Column to sort, there is no Sorting Arrow in the column.' CFSM uses custom filtering methods which prevent the sorting glyph from being shown after a filter is applied. When a filter is applied, sorting still functions, but the sort glyph can not be show. If you clear the filter and then click on a column header the sort glyph will be shown again. This is an expected behavior.