How can I tell whether a scrollbar is visible in my DataGrid is visible
If you are using a derived DataGrid, then you can check the Visible property on the protected VertScrollBar property of DataGrid. So, you could check Me.VertScrollBar.Visible from within your derived DataGrid.
To check it without access to the protected scrollbar properties is a little more work, but possible. One technique is to loop through the Controls property of the DataGrid looking for the scrollbar, and then checking its visible property at that time.