Serges

If I understand right, you already made some changes in the header.php? If yes, did you try to revert it and check the issue?
What theme do you use?
I faced similar issue, when inserted some php code in the wrong place of header code.

Regarding gallery plugin. Will you manage it by yourself or users will also have the possibility to upload photos?
By categories you mean gallery categories, not images categories?
It’s like you need not only the simple gallery plugin, but with some text and not caption, right?

As for membership and different roles, there are plenty of Membership plugins, which you can find here https://www.ads-software.com/plugins/search/membership/
You will be able to set up additional fields, which users can fill during registration or in their profiles.
However, I am not sure, but for calendars and phone books you will also need plugins with some options like displaying content for chosen roles.

So, if you inserted the pictures, they display like
photo0000003.jpg
photo0000002.jpg
photo0000001.jpg?
Did you try to manually drag them? Or you want them to be sorted by name automatically?

Sorry, I don’t fully understand.
You want users to enter product price, title etc and the WordPress theme search will find the product?
Or users must enter the title of the product and search will find product page?

Try to use this search https://www.ads-software.com/plugins/search/Product+Comparison/
I saw some similar plugins.

Do you use nay plugins for mobile view?
I recently have similar issues and the problem was in the plugin, which “tried” to adapt the site for mobile devices.
If yes, then deactivate it, clear all cache and check it again.

By hovering you mean blue light, when you move your mouse on the menu and drop-down list appear?
Did you try to contact theme developers? They probably know and can help you with CSS code to disable hovering animation.

About Image in the menu, check this article https://www.wpbeginner.com/plugins/how-to-add-image-icons-with-navigation-menus-in-wordpress/
Looks like it’s exactly what you want.

Does it happen from the very beginning or you faced this issue after some time (I mean, last week, for example)? If yes, maybe it’s a plugin or theme conflict?
Try to deactivate all your plugins one by one and check the issue. Thus you will find out which plugin causes the error. If it won’t help, try to switch temporarily to a standard WordPress theme.

This is how your link looks for me https://prnt.sc/gmli7m
I see only tablets images and images in the line above tablets(like in the header), but below the footer. And this is some kind of slider.
Do you talk about these images? Maybe it will be better if you show on screenshot what exactly you want to move.
And yes, you definitely can move pictures via standard WordPress editor.
But you want to know about the plugin, which will move pictures from all posts automatically?

How do you insert the table into page? Do you use some plugins? If yes, than what plugin you use?
You can also provide screenshots of how your tables look in the Excel.

As I can check now your “Blog” button, I see the page https://prnt.sc/gml868
Did you fixed it already? Or users should see another page? I can’t tell for sure from your screenshots what I should see.

Looks like here https://wordpress.stackexchange.com/questions/248779/undefined-index-in-wp-includes-class-requests-php is the same problem, but not very “solving” answer.

As for me, the problem is obvious: plugin conflict.
OR maybe this is how WP Smush works (I don’t use this plugin)
You can check your browser console for any errors, when you don’t see your WP media library and then contact plugin support with detailed description of your issue.
You can also post some screenshots of this issue and from console here, perhaps someone faced this issue before.