In administration I can use “Hide in menus” to hide a page from all Menus. But that’s not always the user case. There could be a bottom menu, a side menu, etc., and sometimes you only want to show/hide some item in specific one. Is it possible to tune settings that way? How hard it would be, and can somebody kick me in the right direction. Thanks.
Basically a check box per menu … is not UX wise the perfect solution
You can use a folder with shortcut document for each menu, like this you can configure, sort, … each menu from the backend. And you can use the security policy hide those parts of the tree for simple editor.
Sounds like a plan, but still I want my simple editor to be able to add/remove/sort menu items for multiple Menus. So a “Page” (not folder as you wrote), is a bit confusing. And overall this gives a feeling of a Workaround, not a solid intuitive solution.
Ideally I could insert MenuItem (new thing) inside Menu, if I choose manual (new thing) mode. Then I could configure MenuItem to be a shortcut to some Page or external URL, add rights, etc. 
You can name this document type “Menu” if it make sense in your case, and let the user manager shortcut document below the “Menu” (folder), use node contraints to allow only “Menu Shortcut”, create this new type with all the options you need and that’s it.
PS: On most project, when I heard “User needs to edit/change menu” in a complex way … it’s a red flag for me. Editor should not have to think about menu the system must enforce rules and apply them automatically. And adding tons of options to hide/show in menu is not really an option. Try to think if you can show/hide item in menu, based on Node Type by example, by ex. A “Top News” document type is in the latest news on the home page, but a basic “News” document type is not (and Top News just extend New). This way the editor need to think in term of content and not website structure/organization. And you can change the rule that manage menu with killing the workflow of your editor. Try to go the “semantic way” and not the “configuration hell way” that need a bit of practice, but most editor will love to focus on content.