What may be happening is you’re editing the wrong template. If the shortcode is [ESPRESSO_MY_EVENTS template=event_section]
then you’re editing the correct template.
If the shortcode is [ESPRESSO_MY_EVENTS template=simple_list_table]
then you’ll need to make the edits to the
content-espresso_my_events-simple_list_table.template.php template file. It’s also important that the custom template file is in the correct location. The correct location is in the top level of your active WordPress theme.
With regards to the order, the registrations are listed by the date of registration. So the most recent registrations will be listed last.