You can use the QueryInputKey event on the CellEditorManager, and monitor which key is pressed, an act accordingly.  Note that the up or down arrow should already commit the changes to the InsertionRow.

e.g. :

private void Form1_Load(object sender, EventArgs e)

    foreach( Column col in gridControl1.Columns )

        col.CellEditorManager.QueryInputKey += new QueryEditorInputKeyEventHandler(CellEditorManager_QueryInputKey);

}

void CellEditorManager_QueryInputKey( object sender, QueryEditorInputKeyEventArgs e )

    if( e.Cell.GetType() == typeof( InsertionCell ) )

        if( e.KeyData == Keys.Enter && e.Cell.ParentColumn.Title != "LastCell" )

            gridControl1.MoveCurrentCell( HorizontalDirection.Right );

            e.IsInputKey = true;