The list of orthologs rank is based on their homology score. A gene with rank 1 is the best candidate to be an ortholog. To call it a true ortholog we need to run blast in the "opposite" direction where the matching gene becomes the query and see if the clicked gene appears on top of the list (has Reverse Rank 1). The rank assignment is done offline beforehand and Persephone just displays the results in the grid.
The Choose Columns button enables you to specify what data to display in the table by selecting column names from a drop-down checkbox menu. The Display Map button will open a map for the selected row in the table. Note that only a single row can be selected in the table at a time.