You need to use an optional userChrome.css file to make UI changes such as that going forward.

Here is an example of what's involved: Tutorial - Creating and Editing userChrome.css https://www.reddit.com/r/firefox/comments/6xtm69/creating_and_editing_userchromecss/

Here's a whole bunch more Reddit discussions about userChrome.css . https://www.google.com/search?q=reddit+Firefox+userChrome.css&sourceid=mozilla-search&start=0&start=0&ie=utf-8&oe=utf-8num=100

Basic explanation of userChrome.css from years ago, http://kb.mozillazine.org/UserChrome.css

'kamenvmsk said

In 52 and older versions I could use Menu Wizard, FFChrome, MenuFilter, MenuManipulator addons. All of them don't supported in 57+ and I don't want to turn on "extensions.legacy.enabled" because this option may be deleted in the future.

That preference will not work in the stable release anyway, only in the Developer Edition or "Nightly."

How can I (manually or with an addon) edit the context menus for deleting unneeded lines or for adding some custom lines with a new functionality (for example, "open in an application" - process.runAsync(args, args.length);)?

As the-edmeister describes, you can use a userChrome.css file to hide and sometimes to rearrange elements of the user interface. However, you can't generate completely new functionality that way. An add-on would be required, assuming the missing functionality is allowed in the new higher-security design.

the-edmeister said http://kb.mozillazine.org/UserChrome.css </blockquote> Yes, I know about userchrome.css, but I need some practical examples of serious modification (adding elements using browser functions, reordering items, creating submenus).

jscher2000 said </blockquote> As the-edmeister describes, you can use a userChrome.css file to hide and sometimes to rearrange elements of the user interface. However, you can't generate completely new functionality that way. An add-on would be required, assuming the missing functionality is allowed in the new higher-security design. </blockquote> Does this mean, that from now it isn't possible to manually or via any addons bypass "he new higher-security design" for using functions, which I used earlier?

kamenvmsk said

Does this mean, that from now it isn't possible to manually or via any addons bypass "he new higher-security design" for using functions, which I used earlier?

I was speaking of userChrome.css. "Hide not add" is true now and going forward.

More generally, extensions can add their own item(s) to the right-click context menu now and in Firefox 57+. However, they cannot do everything that legacy extensions did.

I've noticed some extension features require you to install a separate program on the system that the extension can command to perform file system operations. (For example: reStyle) I have not tried any of those types of extensions yet and don't understand their safety implications.

There are a lot of proposals under consideration for future versions, so my comments might be quite different in 6 months when Firefox 52 ESR users are facing the leap to Firefox 59 ESR.