Hello
1. I'll try to add more 😇
2. You'll not find "FILE NAME" itself. The following line adds the column. The column title is somewhere hard coded in Inventor itself or the language packs.
Dim oPartsListColumn As PartsListColumn
oPartsListColumn = oPartsList.PartsListColumns.Add(kFilenamePartsListProperty)
This would do the same as if you were open the parts list edit dialog, open the column chooser dialog and select the file name option on the left side to add to your parts list.

3. Maybe you should post your test drawing with all the referenced files, cause I can not reproduce it.
4. I try to describe the complete function. Maybe there is a missunderstanding.
- define the title of the sheet number column in partslist in "sSheetNumberColumn"
- starting from an open drawing document
- get the first partslist on the active sheet
- traverse all partslist columns and search for a column named like defined "sSheetNumberColumn"
- if column is not found, add it
- traverse all partslist columns again to get the columnindex number of the sheet number column
- traverse all partslist rows
- get the referenced file (the fullfilename)
- call function GetSheetNumber
- traversing all sheets in the drawing document
- on each sheet traverse all drawingviews
- compare the referenced document (FullFileName) of the drawingview with the referenced file (FullFilName) of the partslist row
- if FullFileNames match, add the sheetnumber to the string GetSheetNumber
- if all drawingviews on all sheets are processed, return the GetSheetNumber String
- add the GetSheetNumber string to the cell in partslist row
- continue with next partslist row
I number all sheets in the order they are listed in browser and exclude all sheets which are set to "Exclude from count". Otherwise the automatic sheet number in titleblock would differ.
R. Krieg
RKW Solutions
www.rkw-solutions.com