Hi,
Is there any way I can list all categories with image got from custom field from latest post in each category?
Sure,
<?php
$application->getAllCategoriesWithImageGotFromCustomFieldFromLatestPostInEachCategory();
?>
However, I get the feeling you’re not talking about the application detailed above? To which are you referring?
Wordpress maybe? 
Yes, I meant WordPress 
I’d like to list categories like this:
Category 1 - name
Image from custom field form the latest post in Category 1
Category 2 - name
Image from custom field form the latest post in Category 2
…
Category n - name
Image from custom field form the latest post in Category n
I’d be great if you could find a solution