As I understand it, dogs are believed to have been derived from wolves, over time and with a lot of selective breeding.
What wild animal did the domestic cat come from? does that wild animal still exist?
The Wildcat, of course.
Specifically, the African subspecies. They moved in with us when they realized it was to their advantage. 
Moved to General Questions from Great Debates.
Squee! (Proto)kitty!
Behold, the Ur-Kitty. 
Does it meow?
Some are now breeding the wild African Serval with domestic cats to create the Savannah Cat.
More or less. They make a version of a meow ( wiki lists it as a “mau” sound ) to solicit food from their mother when they are kittens. However domestication may have impacted vocalizations. See for example here.
The standard story about cat domestication is that it happened in ancient Egypt, soon after people there began storing grain in large granaries. The granaries quickly became infested by mice and rats, eating the grain, but the abundance of these rodents there attracted wildcats to eat the rodents. Pretty soon, the people realized what was going on, and started doing what they could to attract the cats and keep them around. People got accustomed to feeding and taking care of cats, and cats got accustomed to being around people and taking food from them. After another few millennia of the domestication process, we wound up with an Andrew Lloyd-Webber musical about them.
Of course, this being the Dope, someone will probably be along soon to tell us this is all a myth.
Not necessarily, but the oldest archaeological evidence currently comes from the island of Cyprus. But that doesn’t mean much. Cyprus has been a trade hub since forever and the origins could indeed be Egypt, though could also just as easily be somewhere else in the Fertile Crescent. Regardless it certainly the case that Egypt were enthusiastic adopters of animal cults centered on the wee beastie.
FWIW, years ago I read a hypothesis/theory/opinion that the skull sizes of lions, tigers and other wild cats, including such extinct varieties such as the sabre tooth, show that domestic cats’ brains, as a percentage of body size relative to their cousins, have shrunk and are still shrinking since their forebears eschewed caves, the savannahs and mountain aeries when they discovered the easy-street delights of no competition, no fear for their lives, three squares and sleeping in their servants’ beds.
No, you have that backwards. They let us move in with them.
More correctly, the African wildcats let our ape ancestors down from the trees when the savannah needed fresh cat litter. They’ve been domesticating us ever since.
I’ve read the cat’s meow has evolved to become more similar to a human infant. Because it takes advantage of humans’ instinctive protect-and-feed response of a baby. It seems plausible to me, but is it true?
Douglas Adams had it wrong. He said it was the mice. Why would it be something we actively seek out and kill?
It’s the cats. They’re the ones who funded this project.
The Wikipedia article on “Cuteness” has a back-link to “pedomorphosis” (aka “neoteny”), which is that precise biological characteristic of retaining juvenile features into adulthood, which is cited as a biological/perceptual psychological basis of “cuteness”. (The page also has a picture of wee Birman moggies, so that’s also good.)
So Wikipedia, as well as its cited references on the subject, seems to agree.
when a mommy cat and a daddy cat love each other very much…
No, I think it is basically correct. Except that people didn’t have to feed them. That would have left them less willing to clean up the rodents. Basically, the grain silos were free lunch for the rodents, but the rodents were free lunch for the cats. It was a lot easier than chasing them in the wild. So it was a win-win situation for the cats and the people. Not so for the rodents. Eventually, the cats evolved to be comfortable with people.
I think it is fair to say that people domesticated dogs, but that cats domesticated humans. Certainly, I’ve never seen a cat go out its way to please me.
So people may have “created” the meow based on what kitties they took home and loved up on vs. what kitties they put in a sack and drowned…