The preferred abbreviation for Firefox is Fx, Mozilla uses it for extension file names. FF is wrong as there is no second capital F in Firefox.
Yes they do. And hardly anyone cares. Except maybe Mozilla.
FWIW, in the USA "Fx" has been used as the abbreviation for "special effects" in the movie industry for ages, and is what most people here immediately think of when they see it.
"Fx" also is the recognized abbreviation for "foreign exchange" in Canada and the USA. Webster's Dictionary lists it as such too.
"fx" has also been a standard abbreviation for "fracture" on medical reports for many many years. Far longer than there has been a Firefox. Or even an Internet for that matter.
So good luck with that, Mozilla! (At least in North America.)