Firefox/Services menu void The items in Firefox/Services menu disappeared after I restart my iMac, but not in every browser tab. For example, they are there and working correctly if the browser display the Help/Troubleshooting page (I'm not sure the name is the correct one, I have a localized version in Italian: "Aiuto/Risoluzione dei problemi").

If I actuate Firefox's refresh function, Services work properly until I close and reopen Firefox.

I tried to run Firefox with the option "-NSDebugServices com.apple.mail" getting the following messages:

Mail/New Email With Selection (com.apple.mail) is enabled in the services menu and disabled in the context menu, by the standard Services policy.
Mail/New Email To Address (com.apple.mail) is enabled in the services menu and disabled in the context menu, by the standard Services policy.
Mail/New Email To Address (com.apple.mail) is disqualified because its send and/or return types cannot be handled by the requestor ChildView 0x11b6e4680, gecko child 0x11ba56800, frame {{0, 0}, {1580, 1040}}.
Mail/New Email With Selection (com.apple.mail) is disqualified because its send and/or return types cannot be handled by the requestor ChildView 0x11b6e4680, gecko child 0x11ba56800, frame {{0, 0}, {1580, 1040}}.
GVA info: Successfully connected to the Intel plugin, offline Gen9 
WebGL(0x12dc38000)::ForceLoseContext"


Please, do you have any idea how to fix my installation?

iMac Retina 5K Late 2015 -
OS X 10.11.6 -
Firefox 50.0.2

After the Firefox 50.1 release updated "The song remains the same"...

but:

Furthermore in other programs, where the Services menu works well, Internet related item like "Search with DuckDuckGo" opens Safari instead of my default browser Firefox (look at the icon near the menu text in the upper picture).
Mac services are only enabled if some text is selected.

Selecting text in Google Docs in Firefox (DE 63) does not enable any whereas selecting text in other pages (including your example, about:services) does.

There may be something broken in how the current selection is communicated to the Services menu.