apparently she got some powers from poison ivy, has shown beyond human strength, agility, speed, stamina, durability and healing. don't know if that all came from poison ivy or not. wiki also has her with genius iq, underwater breathing, and immuity to all toxins and diseases.
Immunity to poisons and toxins is specifically Ivy doing tests on her.
The super strength etc, is just alluded to, from time to time. Its only been directly asserted once or twice. one was an alt Earth.
During, Convergance, one of the Alt earths that was Bottled by Brainiac. the Bottling, turns off superpowers of the inhabitants. when Bottled, that Harley regained some sanity, and lost the ability to pick up her giant mallet.
She can pick up that giant mallet and swing it. takes more damage then any normal human should, etc. Survived all sorts of shit, she has no business to. it is generally accepted she does have some small level of metahuman powers. never quantified, but she is significantly stronger and more durable, then a women of her size should be.
Sanity level varies by writer, canon. Sometimes shes just personality disorder. occasionally, she actually has hallucinations, and full psychosis.
Early life, also varies. Dini had her sleep through college, and fuck her teachers for her degree. but he also had batgirl fuck batman, and get an abortion, so, fuck him sometimes. I'm def on board with Harley earned her degree. it's much more poignant if Harley was a normal person before Joker got his hands on her, then if she was a total fuckup right from the get go.
In canon, her dad was a thug, and got sent to prison. she had 3 brothers. her mom raised her. and she was a bit of a violent helion as a kid. (her fam is still alive, although her mom died of cancer last year.)