Replace URL with Image

Hey there!
I’m trying to find a way to do the following:
– User posts an URL to an Image on my hosted WP as a comment
– WordPress shows The URL, not the image itself

Now, is there any way I can teach WordPress to replace that URL with the image itself (I don’t even need width and height as those are determined by CSS max-width and -height) and Yes: I can trust my users 😉
It should work in Posts and Comments, ideally.

So basically don’t show URLs but Images themselves. It works with Vimeo-URLs, Youtube-URLs and so on, but not with GIF, JPG…… if they come from URLS.

Thanks in advance for your help! I undestand average coding (CSS, Theme-Edit and a slice of PHP) 😉