I'll be honest with you here, one of the MAIN differences between X3 and many other websites (for example wordpress or even Flickr), is that images are stored and sorted physically into folders, instead of sorted in by tags/categories unrelated to any page. There are clear benefits of this in terms of simply creating pages and galleries for a website. With other websites, since images are not related to a page, you would have to "add gallery" to each page where you want a gallery to display.
Having said that, X3 is simply not the best platform if you need to create abstract galleries with categories and tags. This is one of the fundamental differences that will always be a feature of X3. If you want to have galleries from a single section displayed across multiple sections, your options are limited.
This is because if I create a menu in the latest version of X3 with a categories submenu, the only way to categorize the images is to duplicate the same image in different folders.
May I ask how you planned to implement galleries from one page into another using categories/tags?
There is already an option in page settings > gallery >
assets, which allows you to assign a gallery from a different folder. In this way, you can add a gallery from a single page into other pages.
tag/categorize the images (assign tags/categories to the images from the backend and/or extract tags/categories from IPTC) and a search field where a user find the images.
In a future version, you will be able to TAG images. This will have TWO benefits:
1) It will be used for an upcoming "search" feature, and
2) There will be a "filter" plugin, which will allow the visitor to "filter" images in a single gallery based on tags. It is NOT a way to abstract images so you could for instance create a single gallery from images stored in dozens of pages with the same tag.
"Categories" is not be a feature.
We may explore new features in regards to your request. However, X3 is a mainly a platform for creating website pages/galleries, where images are physically linked to the page itself. Do you have an example of a system where you can insert multiple advanced galleries (X3 style) from other pages based on tags and/or categories? The best I can imagine, is perhaps Wordpress where you could insert a simple gallery directly into the "content" section based on tags.