This functionality will be available with Q1 2016 SP.

If I change Column.IsVisibility to FALSE, the column group headers are disappear and not restored.

The problem should be resolved with LIB version 2016.1.404.

The problem should be resolved with lib version 2016.1.125.

When a SortDesciptor is applied and items are modified, the selection behaves inconsistently:

1. If an item is modified, so it's position needs to be changed according to the sorting descriptor, it will be removed from the SelectedItems.
2. If an item is modified, but it's position should remain the same, it remains in the SelectedItems collection.
2a. If IsSynchronizedWithCurrentItem item is set to true and the position should remain the same, the item is removed from the SelectedItems and the one that goes in the same position is added to the collection.

Workaround is to add the item back to the SelectedItems collection when RowEdit ends.

private void clubsGrid_RowEditEnded(object sender, GridViewRowEditEndedEventArgs e)
{
    (e.Source as RadGridView).SelectedItems.Add(e.NewData as Club);
}

When loading the columns from a file the columns are read in the order they are found in the Columns collection of RadGridView upon saving them.
Setting the DisplayIndex triggers the internal grid logic that ensures the DisplayIndex of each column is correct. 
The combination of the above two operations can cause the grid to invalidate the DisplayIndex of columns while deserializing them and thus setting invalid values.
To ensure correct behaviour when deserializing sort the columns by their display order property before returning them in ProvideValue()

The problem should be resolved with Q1 2016.

To work around the issue, set the EnableColumnGroupsVirtualization property of RadGridView to True.