When the Show Full Post button is clicked, Discourse scrapes the page that the post was published from and attempts to find the most readable content on the page. Youtube links are consistently stripped from the post.
I did some tests with this today to see what happens with images. What I’m finding is that whether or not an image is displayed depends on the image’s markup. If I publish a post from WordPress with the new Block Editor, images are not displayed when I click the Show Full Post button. If I publish a post with the Classic Editor - just using a regular img tag, images are displayed. The difference seems to be the extra markup that is added by the Block Editor.