Maybe now you begin to understand the difference, but yesterday you called album what’s actually a gallery, and your album page has always been right without the slideshow link that you said was there. That link was/is only in the gallery pages because you have selected so, that’s OK.
The problem was in the gallery because you had created a double path, and then the second was obviously not found.
The album URL should be: yoursite/gallery, and here you are, and the galleries URL should be: yoursite/gallery/name of the gallery.
“gallery” is the album page that contains all of your displayed galleries, showing only one choosen image by gallery as a cover, “name of the gallery” is a child of that page/album, is a gallery, displayed in another page, the gallery page, with all images of that gallery.
So you have an Album:
A page called “Gallery” like you have or different, with [album id=1 template=compact] e.g., and this is the page base, the parent.
The album in admin doesn’t need no name, it has the id that you call up in the shortcode. In the settings “manage album” you’ve selected album id 1 and you’ve inserted the two galleries.
Galleries:
You have a page for each gallery with its relative shortcode, and in the drop down menu on the right you have to select the page “Gallery” (the album) as a parent.
In the settings “manage galleries” open a gallery, e.g. “Grand opening”, and you should have the title, then next right “link to the page” (I don’t know if it’s written just like that, I use another language), there you select the page you created for that gallery, that’s “grand opening”.
Below, in the “create a new page”, you will have “main page”. The path should be wp-content/gallery/name of the gallery. Same thing for “our place”.
/gallery/nggallery/mswc/our-place/ could be a friendlier and clearer URL: /gallery/our-place, because /mswc/ doesn’t mean anything and nggallery is useless.
/gallery/nggallery/opening/grand-opening/ will become /gallery/grand-opening/ (opening means nothing if you have grand opening, and if you have another opening event you call it with its name).
therefore I chose to put galleries in an Album which is exactly what the album is for
It’s like saying: I have a thing labeled “thing” so I want to put it in a box called “thing”, so I’ll write thing/thing over the box label.
https://www.nextgen-gallery.com/faq/