This expression, whether in its noun form have a beef, or its verb form, to beef, may come down to us from Cockney rhyming slang.
Beef rhymes with Thief
Beeves (archaic) rhymes with Thieves
Imagine a bustling market day. In the narrow streets, a neighborhood pickpocket weaves through the crowd, pursued by a stranger shouting, "Stop! Thief!" Imagine that none too few persons in the market know the thief, or consider themselves bound to him by common interest. To muffle the alarm, the bemused sympathizers call out "Hot Beef!" and amidst the confusion the rascal slips away.
Too fanciful for you? Well, then, if you will, accept only that Cockney rhyming slang is a real phenomenon, without delving into the reasons for its adoption.
From Historically Speaking:
This phrase has been around for a couple of centuries now and comes
from the London criminal underworld.
Well known for its use of cockney rhyming slang, phrases aren’t always
what they appear to be.
The traditional shout of “stop thief!” was mocked by being replaced by
“hot beef, hot beef” in criminal circles where it was thought that the
shouts of “stop thief” were nothing more than making fuss about
nothing.
The 1811 edition of the “Dictionary of the Vulgar Tongue” defines Beef
as: “to cry beef; to give the alarm.”
Here are four related entries from the Dictionary of the Vulgar Tongue (1811):
TO SING. To call out; the coves sing out beef; they call out stop thief.
BEEF. To cry beef; to give the alarm. They have cried beef on us.
Cant.--To be in a man's beef; to wound him with a sword. To be in a
woman's beef; to have carnal knowledge of her. Say you bought your
beef of me, a jocular request from a butcher to a fat man. implying
that he credits the butcher who serves him.
DUMMEE. A pocket book. A dummee hunter. A pick-pocket, who lurks
about to steal pocket books out of gentlemen's pockets. Frisk the
dummee of the screens; take all the bank notes out of the pocket
book, [D]ing the dummee, and bolt, they sing out beef. Throw away the
pocket book, and run off, as they call out "stop thief."
SQUEAK. A narrow escape, a chance: he had a squeak for his life. To
squeak; to confess, peach, or turn stag. They squeak beef upon us;
they cry out thieves after us. CANT.
'Sitters' of various sorts were much in the news in the early 1930s. Tree-sitters, flagpole sitters and house sitters all made appearances. For example, this concerning a long-staying house guest, from the Barnard Bulletin (New York, New York) of 07 Nov 1930:
As his host remarks, "I've heard of flag-pole sitters and tree sitters, but, by God, this fellow's a house sitter!"
Note that flag-pole sitting, tree sitting and, in this case, house sitting, did not connote care for or attention to, respectively, flag-poles, trees and houses, but rather were practiced as faddish and capricious tests or contests of endurance.
The term 'baby sitters', however, so far as I can discover, was coined by or to describe one arm of the "Hop Light Ladies" in 1933, as mentioned in other answers. The "Hop Light Ladies" were a group of female entrepreneurs who, "before the depression were writers, sculptors, painters, interior decorators and business women". Syndicated stories about these depression-era worthies were edited variously. One version states that a
younger group [of the Hop Light Ladies], to be known as "Baby Sitters," will offer their services to supply reliable women at low cost to couples who wish to leave their youngsters in reliable hands at home while they have an evening out.
The Tennessean (Nashville, Tennessee), 25 May 1933.
The phrasing of the article intimates (but only intimates) that the term was coined by the Hop Light Ladies to describe one of their many money-making endeavors.
'Baby-sitter' did not appear in a vacuum, of course. Influences on its development and adoption worth mentioning, other than the above-attested general prevalence in depression-era US news of 'sitters' of various sorts, include earlier use in the US of the slang term 'baby-herder', along with slang use of the noun 'sit' as a shortening of 'situation'.
The somewhat earlier 'baby-herder' and later 'baby-sitter' are in contrast to the now-historical and derogatory 'baby-farmer' (1867), one "who undertakes the charge of children for a fixed sum" (OED). 'Baby-sitter' may well have been deliberately coined with the idea of avoiding entrepreneurial association with the practice of 'baby-farming'.
Add to these influences that 'sit' (the verb) had long been used with appositive complements to denote "the position or occupation of a person" (OED, sit, v., 7c, attested from around 825).
Of the 'baby-herders' and the noun 'sit' meaning "situation", the following evidence pertains.
The slang 'sit' meaning "situation" appeared first, in 1853. Originally, the term referred to type compositers:
sit, n.2
...
slang (orig. Printing).
= SITUATION n. 6b.
1853 ‘M. Twain’ in Hannibal (Missouri) Jrnl. 8 Sept. 2/1 I shall look out for a sit; for they say there is plenty of work to be had for sober compositors.
OED
Use of the slang 'sit' is further attested in OED through 1914. Also, numerous 'Work Wanted' ads of the following general form appear in US newspapers throughout the late decades of the 1800s and the early decades of the 1900s:
(from the St. Louis Post-Dispatch, Missouri, 20 Sep 1912).
The US slang 'baby herder' does not appear in OED. I found a scattering of appearances of the term in US newspapers from 1875 through 1947. The first, from 1875, makes the connection between 'sit' and 'baby herder':
Many of the miners of the Salmon mountains are wintering in the Lembi valley, some of whom have received temporary "sits" as "baby herders", receiving therefor regular rations of substantial grub.
The Independent-Record (Helena, Montana), 16 Mar 1875.
Further appearances (for example, in 1878, 1887, 1888, 1891, 1894) firmly establish that the intended meaning of 'baby herder' is 'baby sitter', and a 1947 appearance in an article listing some of the contents of The American Thesarus of Slang (Lester V. Berrey and Melvin Van den Burk) provides one definition:
A nurse maid is a baby herder or kindergardener.
*The Winnipeg Tribune (Winnipeg, Manitoba, Canada), 23 Apr 1947.
One Spurious 1914 Appearance of 'Baby-Sitting'
The 1914 first appearance date given unattested by Etymology Online may have been sponsored by an OCR error, as shown under About this Book ("Baby-sitting campaigns pliminary report..." at left) in the Google scan of a 1914 US Government Printing Office monograph titled Baby-Saving Campaigns, produced by the US Department of Labor Children's Bureau.
Best Answer
I've come across "femicide" with the "hate crime" meaning, but never "feminicide". If it was commonplace I probably would have seen it despite only reading a little on related subjects.
Here in Britain, "homicide" isn't used as much as in the US, thus "murder" is the standard gender-neutral term. We only need a term for killing someone of a particular group when their membership of the group is important to the fact of the killing (in ordinary use). So "murder" suffices in cases where the gender of the victim is irrelevant or unknown, while "femicide" is appropriate for cases where the gender is important, and "feminicide" unnecessary.
Your second source may use a very specific definition local to a particular field, but I would expect this to be given at the first use in every work assumed at readers outside that field. Otherwise it looks like someone has slipped in an extra syllable - a not uncommon difference between US and UK spellings.