Thanks for your detailed email!
I believe the issue you're experiencing is caused by the "Activate permalinks" option at Gallery --> Options --> General Options. It looks as though you've got this switched on, as it's changing NextGEN's URL structure for things such as the "Show as slideshow" and "Show picture list" links, as well as navigation through your Album pages.
I've coded Optimizer Premium to look for NextGEN's default URL structure, which appends query string parameters to much of the navigation. With "Activate permalinks" switched on, these parameters are no longer present, which results in the plugin not recognizing where to add the necessary scripts for both Fancybox and slideshow functionality.
Here's an example from my testing environment:
Default album gallery / show as slideshow link / show picture list links:
Custom album gallery / show as slideshow link / show picture list links:
I'll have to find a way of targeting these custom URLs in a future version of the plugin, but for now, correcting the issue is as simple as navigating to Gallery --> Options --> General Options, switching off the "Activate permalinks" setting and clicking "Save Changes".
Note: I STRONGLY advise making a backup of your entire wp-content/gallery folder just in case...I lost all my images after testing the "Create new URL friendly image slugs" button below it. You won't need to use that button, but it's still good to have a backup.
Hope this helps!