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Good to hear from you again, and thanks for your question. Thanks especially for including the full text of your shortcodes; very helpful.
To make pagination work in synchronization with a gallery display the data selection parameters of both shortcodes must be identical. Your gallery shortcode contains my_custom_sql="attachment_category='Airone guardabuoi' orderby=date order=DESC", but the pagination shortcode has a slightly different attachment_category="Airone guardabuoi". If you copy the parameter in the gallery shortcode to the pagination shortcode (or the other way around) they will be in synch.
I went to the page you gave a link to and had a look. I count 29 items in the gallery display. Since this is less than the posts_per_page=30 value, no pagination controls will be displayed. I also see that the page lists “39 immagini” so I imagine you are expecting more images in the gallery. I cannot account for the difference; you will have to investigate further to resolve it. It’s possible that the [numero-specie-pag categoria="Airone guardabuoi"] shortcode is looking in a different taxonomy than the [mla_gallery] shortcodes.
I am marking this topic resolved, but please update it if you have any problems or further questions regarding the suggestions above. Thanks for your continuing interest in the plugin.