Among my current skins, a couple of them tick most of your boxes: Neptune and Saturn. Saturn has more traditional thumbnails (borders, shadows, etc.), while Neptune uses a leaner thumbnail display (justified or fixed shape, no shadows, only a thin 1px border option).

Both support metadata - see, e.g., https://jgromit.com/saturn/metadata/. Hover on the little camera icon. Neptune works the same way.

Both have a slideshow, but no autostart. An autostart slideshow is somewhat out of favor - it's considered a little aggressive.

Both have a copyright line option.

Both can show a shadow on the slide image.

No thumbstrips, I'm afraid. They're a huge problem for a responsive layout.

No easily-created external links. I got tired of seeing albums that looked like link farms, with, oh, by the way, an image or two.

But you can use the "top info text" option in either skin to put whatever you like above the thumbnail table. For simple links to other pages, it would take only a few lines of HTML and CSS.

All your requirements have been implemented in the FancyBox skin.

jGromit, thanks for the demo, it works and saved me quite some of time.
AndreWolff, thanks, I will have a look at FancyBox too.

I tried to do it as you suggested, with a div between the links, but then the links ended up in one line each, e.g. three lines with one link each, instead of all links in one line. That's not what I wanted.
The centering looks fine to me.

Sorry, my fault, I didn't read your second post carefully enough. I will change the code accordingly. Thanks again for the great support.

Yes, there is a reason, and it's very complicated. The underlying display script has some unusual behavior when it's set to do a timed slideshow, and that behavior conflicts with the Loop slides setting in the skin.

I need to take another look at that. I think there may be a better solution, but I need to do some experimenting. I'll make a note to come back to that issue.