Delete All Places in ‘’

1. Add this to your CSS:

#geodir_wrapper .entry-title {display: none;}

That will maybe also hide some other headings on other GD pages though.

2. I am not sure what you mean,, but if you want to replace the link text from “Website” to the name of the listing, add this to your functions.php:

add_filter( 'geodir_custom_field_website_name', 'geodir_change_website_field_display_name', 10, 3 ); 
 function geodir_change_website_field_display_name($name,$website,$post_id){
if($name=='Website'){return get_the_title( $post_id ); }
else{return $name;}
 }

Let us know how you went.

1. Do you only want to remove “All Places in” but you want to leave the rest of the heading, or do you want to remove the total heading?

2. Can you explain this better? Give us a URL (you can do that in a private message if you like).

You could remove the “all places in” by changing to a blank string in your translation file.

http://docs.wpgeodirectory.com/translate-core/

Thanks

Have a look at GD > permalinks.
What do you have for “Listing url prefix”?

You cannot remove the postname (catalog), because that is the custom post type slug.
This is because this is the structure:
/postname/category/subcategory(optional)/post-title

If you use the Custom Post Type addon, /postname/ will be the slug of the post type for example
/events/concerts/pink-floyd
/restaurants/italian/pedro