There are dozens of origin stories. The Killing Joke (2014) goes the "one bad day" angle.

I personally prefer the Heath Ledger Joker as the best Joker.

He has no origin and he has no motive. He's just a crazy MF'er that is intent on causing as much chaos as possible for his own amusement.

(Granted I did see a fan theory a few years ago that argued that there is evidence that he was an integral member of the League of Shadows, even possibly their lead explosives engineer. He either got tired of waiting for them to strike or got kicked out for being to crazy for them. I liked that theory too.)

As a comic book character Joker and his origin has many variations. The most common is that he was already a depressed low-level criminal (red hood). He gets chased by batman and falls into a chemical vat that results in the white appearance and green hair. The further societal exclusion makes him blame Batman and society which then becomes a feedback loop.

Joker has had strong implications with Harley Quinn (she was never solo in early work) and some others.

Killing Joke is more or less the approved origin story, although DC tries to be cagey about it.

As far as women goes, he was with Harley for a while, introduced in the animated show then made the jump to comics. Replaced with Punchline.

The Killing Joke is the closest thing to a canonical origin story, but like jordan and RoidingOldMan said, DC doesn't make it clear if that is official.

Personally, I like the idea of him not having a known backstory. It makes the Joker be to Batman what Batman is to most villains. The reader gets to know who Batman is, but to most characters in the DC universe, he's an unknown person with unknown reasons for doing what he does. The Joker is that same thing for Batman.

I know it's likely not canonical, but didn't joke find out Batman was Bruce Wayne in Harley Quinn? I have some kinda memory of joker being upset about it.

2014?! That story came out in 88.

Movie year.

Yes, I'm remembering him yelling, "Where's my damn electric car, Bruce?!"

The whole point of The Killing Joke is that Batman and Gordon prove that the 'one bad day' excuse is full of crap. People seem to miss that, including DC writers.

"Has Joker ever been shown being with a woman?"

Uhhhhh.........Harley Quinn in the corner looking pissed off. Then again, she's also depicted as being Poison Ivy's love interest. So, maybe you didn't think of her because of that. What's even weirder is, Poison Ivy has been shown to flirt with/implied sleeping with Batman, Catwoman has been shown to be sleeping with Batman. Hell, even Joker has said some things that make you think there's sexual tension between them. Yet, I never remember Harley Quinn ever trying to sleep with Batman. I know she tries to sleep with Nightwing, and gets horny when she see's his butt, but I don't remember her ever looking at Batman that way, and she's the only female I can think of that doesn't want to sleep with Batman. Even Barbra Gordon/Batgirl got it on with Bats.

As far as Jokers backstory.....yes, technically. There were 2 movies about Joker. They suck. Nobody considers them canon. Not because we don't want to know Jokers history. It's just we refuse to put any weight behind THAT being his backstory. He's a depressed failed comedian with a medical condition that makes him laugh. There, I just saved you about 4 hours.

I like to believe that Joker has no backstory, and any backstory given can't be trusted as reliable, because the narrator (in this case Joker) is unreliable as a narrator. He's likely to just make anything up, and the words cannot be trusted. Would you like to see how I got these scars?

Man.....1988. Just think......every issue of that comic came with unadvertised trace levels of cocaine. Not because of some promotion or anything. Just because it was 1988. EVERYTHING was coated in a trace layer of cocaine. It was just in the air at all times. I was born in 1983, and I have barely any memory of the 1980s. Coincidence? NO! It was all that cocaine in the air I was breathing! This also explains why I'm stupid. Yeah.....yeah, let's go with that.