Hello and welcome to 4images forum.
Replace in new_images.php
WHERE i.image_active = 1 AND c.cat_id = i.cat_id AND i.cat_id NOT IN (".get_auth_cat_sql("auth_viewcat", "NOTIN").")
With this:
WHERE i.image_active = 1 AND c.cat_id = i.cat_id AND i.cat_id NOT IN (".get_auth_cat_sql("auth_viewcat", "NOTIN").")" . ($cat_id ? " AND i.cat_id = $cat_id" : "") . "
After that you can use cat_id url query to specify a category: http://example.com/4images/new_images.php?cat_id=123