I mostly agree with your definitions. I have some expansions, and then some numbers.
SF can be an umbrella term encompassing science fiction, fantasy, and horror (and their relatives). Or SF can just be an abbreviation for science fiction (which is how I'll use it in the rest of this answer -- I'll use SFFH for the superset). The intended meaning is usually clear from context.
Speculative fiction can be the SFFH umbrella above, opened up. More often (IMHO), speculative fiction is used to distinguish SF (and other SFFH, but mostly SF) that's more self-consciously literary, usually by attempting to go beyond pulp adventure. Spec fic in that sense may have:
less emphasis on science -- and lots less emphasis on gadgetry; societies that are interesting and complex; characters who are well-rounded rather than cardboard cutouts; and style that's more literary. Fancyclopedia 3 (a highly-recommended fannish reference) has elements of both senses, defining speculative fiction as "Any fiction of a speculative nature, but especially science fiction, fantasy and horror that feels embarrassed when it is called science fiction, fantasy or horror."
Science fiction -- yep. Defining science fiction is a fun game, so I could spend all day fussing around with your definition (here, add a pinch of alternate multiverse; over there two dashes of science -- if you're out, you may substitute the articial ingredient sciencey-ness ... ). But I probably would end up making the definition longer but not any more accurate.
To make things more confusing, science fiction sometimes is used to mean SFFH, just like SF and speculative fiction. I believe this usage is declining. The field's leading writers' organization, SFWA,
was originally named Science Fiction Writers of America. At that time, the distinction between science fiction and fantasy was less important and SFWA’s name was accepted as encompassing both.
Later, the name of the organization was changed to Science Fiction and Fantasy Writers of America, although the acronym SFWA was not changed.
Sci fi -- spot on, although the pejorative connotation is declining. The decline was slow after the mid-1960s, and faster after 1992 -- especially among fans and writers of visual media. Some pronounce it skiffy when they want to emphasize the pulpy/B-movie sense.
- Isaac Asimov said in 1978, "We can define "sci-fi" as trashy material sometimes confused, by ignorant people, with s.f. Thus, Star Trek is s.f. while Godzilla Meets Mothra is sci-fi."
- Marion Zimmer Bradley said in 1993, "nobody in the actual field ever says 'sci-fi'..."
Let's look at some actual numbers from some great resources for sf/fannish history. Fanac.org and eFanzines.com aren't a complete corpus of everything fannish, but they're pretty damn good. (Both sites focus overwhelmingly on written SF. Alas, I don't know of similar places for media fandom.) This won't tell us how the terms are used within the SF community, but it shows how popular they are (For how, see the boldfaced SF Cites links above). I searched for phrases on each site (like this:
site:fanac.org "science fiction"). Dates are mostly from SF Citations.
First use Fanac eFzine phrase
--------- ----- ------ -------------
1851/1927 2820 3460 science fiction
1929 2100 3210 SF
1954 374 921 sci fi
1889/1948 189 399 speculative fiction
1916 33 205 scientifiction (clunky Gernsback coinage, generally superseded by "science fiction")
1931 251 321 stf (abbrev. for "scientifiction", either nostalgic or very old-school)
1976? 64 185 skiffy (joking -- well, half-joking -- pronunciation of "sci fi")
1975? 0 1 structural fabulation (an academic term)
Late edit: Links for boldfaced terms go to Science Fiction Citations, an excellent site done by the Oxford English Dictionary for crowd-sourcing first uses of sf terms (many thanks to user14111 for pointing it out). It has definitions, dates of first use, and many examples showing how usage may have evolved. Science Fiction Citations is the precursor to (and occasional follow-up for) the highly-recommended Brave New Words: The Oxford Dictionary of Science Fiction.