"Edit Menu" could be correct if it is a proper noun
If the menu is officially named something like "Edit Menu", it is a proper noun and capitalization is correct. If the menu is not officially named that, then it is not correct to write "Edit Menu". Same goes for "Menu Bar"—if this is officially defined as the name of a certain part of the interface, that's its name. People are free to assign proper names to just about anything, as far as I know. (But personally, I think this style looks a bit silly.)
"Edit menu" could be correct as a common noun preceded by a "quote" of the literal text used to label the menu
However, it seems your peers are not using "Edit Menu" as a proper noun, but instead refering to the menu by taking the common noun "menu" and preposing the word that is used to label this object. Looking at my screen, this sort of label is capitalized in the Mac user interface:
But not in the Stack Exchange one:
So it might not make sense to use a capitalized "edit" when talking about the Stack Exchange interface, but it would when talking about the Mac interface.
In a more explicit style, this type of labelling could be indicated with quotation marks: the "Edit" menu (="the menu that says "Edit"). Another possible convention is bolding (the Edit menu). A third possible convention is to use a monospaced, or otherwise distinct typeface (the
Edit menu). Any of these could be correct; it all depends on the style defined for the document. In this context, "Edit" is not capitalized because it is a proper noun, but because this is how the word appears in the object that you are referring to (just like how "T" in "T-shirt" may be capitalized because it is being used to refer to the way a capital letter "T" looks). Of course, for Stack Exchange, it would be most appropriate to write "the edit button" or "the
(Incidentally, I can think of no circumstances where it would be a good idea to write something like "the Edit Menu" or "the
Edit Menu", since proper nouns generally don't have special styling or typefaces associated with them in formal contexts.)
Since menu bars are usually not labeled with the word "Menu", the preceding "label" explanation doesn't work for them in most cases
I just realized that a "menu bar" usually doesn't have the word "Menu" written on it, so by the logic I gave above, it wouldn't normally have a reason to be capitalized (unless it has been offically been given the proper name "Menu Bar"). I decided to look at what some websites do.
The first two sites I found do not capitalize it:
In Microsoft Windows, the menu bar is beneath the title bar. [...]
If the File, Edit and View menus are missing, it is usually because Firefox is in full screen mode or it is not the selected application. [...] Your Mac will always display the menu bar for the program that's currently selected.
This a tiny survey, so if this is an important issue for you you should do more study, but my tentative advice would be to not use the capitalization pattern "Menu bar" unless the bar is literally labelled with the text "Menu". Use either "Menu Bar" (if you've decided to treat it as a proper noun) or the all-lowercase "menu bar".
"fiction writer" and "blue button" would almost never have capitals
As for the additional examples, of course you would write "fiction writer" and "blue button," unless you mean to refer to an author labelled with the word "Fiction" (written with a capital "F"), or a button labelled with the word "Blue" (written with a capital "B"). In fact, if you have a button labelled with the word "Blue" that is not colored blue, it would probably be confusing to refer to it as "the blue button" rather than as "the Blue button" (although "the 'Blue' button", "the Blue button, or "the
Blue button" would be even better).