Most of Jack's actual history can be found on her entry on the MEWiki, but that site doesn't allow for subjective analyses of characters.
Jack acts the way she does because it has kept her alive. I think it's that simple. Her abrasive, confrontational personality and rough appearance allow her to intimidate people and to keep them at a distance. She tells us that each of her tattoos has a meaning. Some she got done herself, others likely have a surgical significance to the doctors who worked on her at the Teltin Facility. Some of her scars are hidden by tattoos. Oher scars are shown plainly. Make of that what you will.
Jack has been taught by the harshness of the galaxy that everyone is only out for themselves. Killing someone increases one's chances of surviving, because that's one less person trying to kill her.
Jack has been taught by the people who took advantage of her that people only deal with other people because they want something. That something usually involves money, her biotic abilities, and sex.
When Jack was a young teenager, after she escaped from Pragia, she was passed around by mercenary companies, probably for sex. That has greatly affected her view of sex. Jack was also likely raped on Purgatory and in other places, further inhibiting her ability to view sexuality as a positive thing that can have nurturing qualities.
If Renegade Shepard takes Jack up on her offer of casual sex, he confirms for her what she thought was the case. If he doesn't take her up, he shows her that it's not sex he wants, but something else, and that confuses her, and makes her wary.
Jack's relationship with Murtock taught her that people might genuinely love each other, with no ulterior motives. She's found that love doesn't necessarily qualify as an ulterior motive. Love is something that defies her conception of the way the galaxy works, and it is a very tender subject for her, especially after what happened to Murtock. She states that Murtock just used her as well, but that may just be her way of rationalizing the situation to fit her perception of the way the galaxy works. It might just be a defense mechanism that protects her from the pain of genuine loss.
Jack says that she gets a warm feeling when she fights. She may love to fight and to kill and to see things tossed about like ragdolls because of her biotics. This may be because of what Cerberus did to her, or because the ability to fight became vital to her in her attempts to stay alive.
Jack is, at first, resistant to believing the records she finds during her loyalty mission. She believed that the riots began because of her. She believed that she had it the worst out of all of the children at the facility, but that wasn't the case. The other children were experimented upon, drugged, frozen, killed and dissected, all so that she, herself, wouldn't be killed by Cerberus' scientist's attempts to create the most powerful human biotic to ever live. Eventually, Shepard can help her to, more or less, get over herself, and put her past behind her.
Jack has a tender side that Shepard gets to see during her final romance scene. I don't know if sincere love is what she's wanted all along, but she seems very relieved to have finally found someone who has no ulterior motives, and who will accept her for who she is. Jack is also the tender person who loves to cuddle, as we see at the end of the scene, but it is highly unlikely that she would show that side of herself to anyone other than Shepard, as it would mess with her ability to keep up appearances.