How to edit/delete single row items in a table on my own menu page

WordPress allows you to use a class called wpdb

Here is an example of how you would use it
function add_to_db() {
global $wpdb;
$your_table_name = $wpdb->prefix . "wp-LINKS-list-table";
$the_value="123";
$wpdb->insert( $your_table_name, array('column_name' => $the_value,));

this will insert 123 into the column_name. You can read more here

Note: If you are creating a menu page that reflects the tables similar to the wordpress tables there is another class you can use to help you. It is called WP_List_Table I would suggest reading that and getting the Custom List Table Example Plugin it is very helpful showing examples of using WP_List_Table.