Use twig to style a specific block (unformated list)

Ok I got it. I've already overwritten form templates to add a template suggestion that included the form id. Here's the code :

function hugo_theme_suggestions_form_alter(array &$suggestions, array $variables) {
    if (isset($variables['element']) && isset($variables['element']['#type']) && $variables['element']['#type'] == 'form') {
        $original_theme_hook = $variables['theme_hook_original'];
        $suggestions[] = $original_theme_hook . '__' . str_replace('-', '_', $variables['element']['#id']);
    }
}

Maybe you could reuse this piece of code changing the form by the view, something like YOURTHEME_theme_suggestions_view_alter

Not sure to understand what you mean...

Do you want to customize the fields that appear in your block?? If so, Drupal normally provides you with available twig hooks you could use. Yours would probably be field.html.twig.

Exemple : you can customize a menu with menu.html.twig and then customize the links in that menu with links.html.twig