My coding skills are very minimal, and I can’t seem to find & edit the HTML.
This is because video embeds are usually implemented using a shortcode, there is no HTML to edit, it’s generated on the fly
Starting playing automatically WITHOUT the user having to click any sort of play button.
yes and no… you can tell the shortcode to specify autoplay like this:
But the browser will probably prevent this unless you meet a number of restrictions. For example, having no sound. Different browsers may have different rules.
Note that autoplaying will use mobile bandwidth, and that the browser or device may be unable to play the video due to its format.
Play on a continuous loop
Yes, add the loop parameter:
https://wordpress.org/support/article/video-shortcode/
Hide the progress bar (including sound and full screen options) at the bottom so it’s just the playing video we can see.
This can be done using CSS alone, just inspect the parts you don’t want and write a CSS rule with display: none;
Note that Divi may be providing its own video player, consult the divi docs ( divi support is offtopic here ) if that’s the case