The etymology and origin of the term has been answered by Hugo so I will limit myself to answering the first two questions.
Why are women called chicks? Is there a negative connotation...
Chick is considered by many women a derogatory term. Why is that? Probably because its primary meaning is that of young bird especially of domestic fowl, more commonly a baby chicken, if you will.
But wait a minute, chicks are pretty fluffy yellow things, they symbolize spring, re-birth, and they are adorably cute too, so the term should be seen a compliment. It might be until we realize that the idiom, "bird brained" refers to a person regarded as silly or stupid. And chickens are famously recognized as being stupid animals. Therefore, chick can describe a pretty (and usually) very young female, but it also implies that the woman is vacuous and empty-headed.
Overall, chick, I would argue carries more negative connotations than positive ones.
I have actually seen witch used in a male sense as well.
If we look at etymonline, it gives the following definitions:
Witch
Old English wicce "female magician, sorceress," in later use especially "a woman supposed to have dealings with the devil or evil spirits and to be able by their cooperation to perform supernatural acts," fem. of Old English wicca "sorcerer, wizard, man who practices witchcraft or magic," from verb wiccian "to practice witchcraft" (compare Low German wikken, wicken "to use witchcraft," wikker, wicker "soothsayer").
(note that the entry is much longer and that the origins are actually not very clear!)
Wizard
early 15c., "philosopher, sage," from Middle English wys "wise" (see wise (adj.)) + -ard. Compare Lithuanian zynyste "magic," zynys "sorcerer," zyne "witch," all from zinoti "to know." The ground sense is perhaps "to know the future." The meaning "one with magical power, one proficient in the occult sciences" did not emerge distinctly until c.1550, the distinction between philosophy and magic being blurred in the Middle Ages. As a slang word meaning "excellent" it is recorded from 1922.
There seems to have been, based on the assumed origins, a difference between "good magic" linked to knowledge and wisdom for wizard, and "bad magic" linked to "heathen practices".
It seems far-fetched to actually take wizard simply as a male version of witch and vice-versa. The etymonline entry for witch, as well as the OED (thank you Peter Shor) show that the male version of wicce was wicca. They were people involved in witchcraft, magic — supernatural things, rather than wisdom (wizard).
They seem to denote similar but different occupations, one of which became mainly associated with man, the other with women.
About the negative connotations that surround the "female" version... yes, that is sexist. And this is a very common occurrence in (many) language(s). Even though (and I am glad) this is often frowned upon by many people nowadays, and many speakers tend to avoid making distinctions between male and female practitioners of the same profession, in the past it was very common to see a clear (quality) distinction between the male and female versions.
Even nowadays, if one reads these lines:
John is a secretary.
Mary is a secretary.
There will be plenty of people assuming that John sits on a board or a committee, while Mary is a personal assistant. (The distinction is even "worse" in languages that use a distinct version of the word, like in Dutch "secretaris" and "secretaresse" — the latter is grammatically the female version, but in reality denotes a different job!)
Compare also "steward" to "stewardess".
It is a simple fact that language exhibits sexist (and sometimes racist and otherwise discriminatory) tendencies. That may be unfortunate, but it should be hardly surprising.
Best Answer
I read years ago that muleteers of the Old West were such experts with their long whips that they could snap a horsefly from the ear of a mule in their team without touching the mule's ear. In such a man's hand, a whip could cut into a mule's tough hide; hence the name mule skinner.
John S. Farmer, Americanisms Old and New: A Dictionary of Words, Phrases and Colloquialisms (1889) includes this entry for mule skinner:
And Stewart Sheldon, Gleanings by the Way, from '36 to '89 (1890) writes:
As Matt Эллен notes in his response to the poster's question, the first citation for mule-skinner is John H. Beadle's Life in Utah; or, The Mysteries and Crimes of Mormonism (1870)—a book whose publisher touts it on the title page as "being an exposé of the secret rites and ceremonies of the Latter-Day Saints, with a full and authentic history of polygamy and the Mormon sect from its origin to the present time." In the book, Beadle writes that mule-driving "mule-skinners" and oxen-driving "bull-whackers" had different levels of social status on the range:
The earliest mention of bull whacker I found in a Google Books search was in a January 1861 article for Hunt's Merchant Magazine and Commercial Review titled "Commerce of the Prairies," by an uncredited author:
A close second is Thomas W. Knox's article, "To Pike's Peak and Denver," for the August 1861 issue of The Knickerbocker magazine:
To these two categories of drivers, George A Crofutt, Crofutt's New Overland Tourist and Pacific Coast Guide (1884) adds a third: "burropuncher."
I haven't come across a comparable name for a horse driver, indicating perhaps that horses were more tractable than bulls, mules, and burros.