I believe that even if it were GPL licensed you could do that, since you’re only running it on your server, not publishing it. Of course, for this very reason, most copylefted server software uses the AGPL, which does require source code of a network service to be made available.

While this is true, it’s also worth noting that the original is permissively licensed. You can change it if you want, it’s just that most people don’t bother. Presumably changing the image would be as simple as replacing the three files in /web/static/img, but maybe that would look weird for some reason.

Edit: Oops, I assumed an Earth day is 1 second instead of 86,000 seconds

I don’t think that one’s been made for Youtube yet.