Custom Post Type Templates from Plugin Folder?

I’d like to offer my custom post type as a Plugin, so that people can use it without touching their theme folder. But custom post type templates — such as single-movies.php — reside in the theme folder. Is there a way to get WP to check for a single-movies.php in the plugin’s folder? Hooking a function into the Filer Hierarchy? Or get_template_directory(); ?

How to move page template files like page-{slug}.php to a sub-directory?

I want to move page template files like page-{slug}.php to a sub-directory within my theme, in a way that WordPress will recognize them automatically. If the page templates of the said form doesn’t exist within the sub-directory, then WordPress should fall back to the default template loading rules. How can I achieve that?