Hello, WordPress supports the YouTube natively, one does not need to add any code, except for CSS decoration. If your problem (a border around a video) is just a CSS, then it will be very short task. As for the link under a video - usually you add it manually (either way), and the only thing you might be concerned about is a CSS decoration. Again, it shall be a very quick fix.
If you think you could figure the CSS all by yourself, then do not choose me. Otherwise I'll need to take a look at the URL before committing to this quick task.
* * *
Many years experience with coding Responsive themes for WordPress from scratch (also: custom plugins, shortcodes, widgets etc), setting up WooCommerce sites, and migrating customers' websites into WordPress from any other formats. Free 2 month support at the end of a project.