Proper meaning of the slang "Baby"

Let him do it because it's his baby.
Don't push this job on me because it's your baby, not mine.
This classic show car is his baby.
Hey baby, how are you doing today?

I understand that the speaker used the word baby to describe work in the first and second examples. The 3rd example is confusing me. How can a car be one's work? Please help improve my understanding.

I know the slang word baby means "a woman who is young", as in the last example, someone is talking to a woman/girl.

You've slightly misinterpreted the word baby in your first three examples. It means something in which one has invested time, interest, and emotion and for which one has a proprietary feeling. Speaking hyperbolically, it's as though the object of interest is like one's own child.

I thought I should add an example of the usage that didn't involve work- or job-related situations. This turned out not to be as easy as I thought. There's even a canonical political cartoon, showing Hoover turning over the problems of the Depression to Roosevelt in 1933, captioned "It's his 'baby' now":

enter image description here

But I finally found a story about a man who as a hobby, salvaged his car that had been in an accident, replacing the metal body with one made entirely of wood. From that story:

So, he started salvage [sic] spruce wood from construction sites, adding up bit-by-bit to his truck every evening after work for about nine months. So you can say it’s his baby now.

A labor of love, with a play on the nine-month "gestation" period for the "baby."

Baby in the first three sentences means:

Slang An object of personal concern or interest:

while in the last one it refers to:

Sweetheart; dear. Used as a term of endearment.

(AHD)

The term baby: (Etymonline)

dates back to the late 14c., babi a diminutive of baban.

As a term of endearment for one's lover it is attested perhaps as early as 1839, certainly by 1901; its popularity perhaps boosted by baby vamp "a popular girl," student slang from c. 1922.