Easy Add Thumbnail

No. This plugin uses only standard WordPress functions to set the featured image. And using this standard (and friendly) method WordPress simply has not any knowing about images not attached to the post.

In that post edit screen, click the “Add Media button”, then click to “Media Library” tab, and select “Uploaded to this post” in the dropdown, you must see at least one image. If you see the “No items found.” message, that means that your images were not uploaded within that post. And therefore, the plugin can’t use any image to set as feature image.

If you can see images when selecting “Uploaded to this post” but the plugin is not using it for feature image. You need to try for theme/plugins conflicting. Try using a WordPress default theme (i.e. Twenty Fifteen) and disabling all other plugins.

As stated above this plugin uses standard WordPress method to set the featured image, this does not include any size information. The size used by your theme for displaying image thumbnails depends totally on how your theme was coded.

Contact to your theme author for support if you’re having this problem.

You can find more information about how to properly show thumbnails in your theme on codex reference for the_post_thumbnail (check ‘Thumbnail Sizes’ section) and set_post_thumbnail_size functions.

If you don’t want to use Easy Add Thumbnail for your pages or any other post type, you can exclude them by simply adding a little snippet of code to your theme functions.php file before enabling the plugin.
The following example will exclude pages:

add_filter ('eat_exclude_types', 'my_excluded_types', 10, 1);
function my_excluded_types ( $exclude_types ){
    $exclude_types[] = 'page'; 
    return $exclude_types;
}

If you want to exclude a custom post type you need to know the value of ‘name’ used in register_post_type() function for registering that post type.
e.g. If you have a custom post type and its ‘name’ is ‘book’ the you’ll use:

add_filter ('eat_exclude_types', 'my_excluded_types', 10, 1);
function my_excluded_types ( $exclude_types ){
    $exclude_types[] = 'book'; 
    return $exclude_types;
}

If you want to exclude more than one post type just duplicate the $exclude_types[] line for each one.

This snippet must be added to your site BEFORE enabling Easy Add Thumbnail in your site,
if you add it later it will stop assigning the thumbnails for new posts in the excluded types after that moment, previous posts will not be modified.

Yes. When I released first version of this plugin years ago, featured images was named as post thumbnails, but later WordPress team decided to change the name to “featured image”.

In fact, WordPress core functions for featured image, still uses original thumbnail names.

That’s because the plugin name (that can’t be changed in the Extend directory without having issues) says “thumbnail”.

Maybe, but WordPress installs older than 4.7 are not supported by me. Try at your own risk.