Thanks for your reply.
Ok for the images that are still there when deleting a gallery: they must be deleted from the pop up. Understood.
The first problem remains, even changing browser, even after the cache was empty. I am not speaking about shortcodes.
I try to re-describe the issue.
I have a PAGE, where in the sidebar there is the widget with ad album. That album contains 2 galleries. One gallery was renamed. When clicking on it in the widget, it opens the gallery in a new page. At the bottom of the gallery there are 2 links: on the right to another gallery, and on the left in another gallery. The left-link points to the gallery that was renamed. As if now there are 2 galleries (that are the same one!) with different names.
Trying to understand the issue, I decided to completely delete one of the 2 galleris of the album. Now, correctly, in the widget there is just one gallery because the other one was deleted. If I click on that only-one gallery remained, it opens the new page with all the images. But… in the link at the bootom of the page, there is again the name of the gallery that was deleted. If I click there, there is the page with the title of the gallery (that was deleted!) but says that simply the gallery is empty. And at the bottom of this page, there is also the link to the gallery that was renamed.
It seems that when you rename the gallery, it creates a new one with the new name, while the old-named gallery becomes empty but still remains. And the same if I delete one gallery: it becomes empty but still remains.
Hope you understand the issue from my words. Can you help me?