If i go to an album page on my zen photo site (for example: http://danturkel.com/gallery/index.php?album=test-gallery ) and then click the link that's supposed to take me back to the gallery page, the link is broken. The link SHOULD go to danturkel.com/gallery/index.php but instead it just goes to danturkel.com/gallery/ and this doesn't work.
How do I fix it?

Then add the full path to the admin options for the gallery home url. Your hosting service seems somehow not support "index.php" as a automatic start page, you might ask your host on that, too.

All I see is an option to change the URL of my home site, but not of the album selection page. Where is this option specifically?

Ah, sorry for confusing, I indeed confused it with the website url myself... I suggest you talk to your host about it.