Boy, was I wondering the same thing! What exactly was her plan?
Interesting theory. If true, she’s a pretty “low budget” operator, judging from the motel she was staying at…
I think her plan was just to slip away before authorities and media got involved. She could probably fake her way on any rescue boat with her falsified ID, although there would be the problem that Walt and Michael would be calling her “Kate” – and unless she stayed on the raft to wait for the second passing ship to pick her up… 
On the assassin thing, I don’t really think it’s anything that complex. (And, as John Mace just said, she would be a pretty low-budget operator in that case!) I think a telling clue was when Kate and Tom were listening to their old cassette tape:
Young Tom: You always want to run away, Katie.
Young Kate: Yeah… And you know why.
I think the molesting and/or abusing father theory is probably the closest guess made so far. And I’m still thinking that she killed her father (probably once she was 18 or so, or at least 16 – would make more sense than if she did it as a minor, where there may be limitations on her ability to be prosecuted for it). Probably in self-defense or to stop the abuse, but others (including Mom) believe otherwise. I can’t think of too many other reasons for Mom to be that scared of her. And it certainly sounds like Tom knew about whatever was going on when they were kids.
I think it was the mother who was abusive, and that Kate had a good relationship with daddy.
She said it was her dad who taught her to hunt and track - I wonder if that was the truth, or part of her spy or assassin training.
I’ve been thinking about this. I’m not sure that I agree with the “Kate killed her abusive father” camp. Reasons in no particular order…
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Kate is convinced that if she gets caught she will go to jail and no one will believe her side of the story. A woman killing a sexually abusive father would probably qualify her for sainthood for about a third of the population and certainly would be something she should be able to convince people of (we know how good she is at manipulation and persuasion). So, whatever it was, it has to have been something that most people would consider to be “wrong” and something that there is enough evidence against her for that she has virtually no chance of talking herself out of.
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No matter what the reason, her killing her father would simply be a murder investigation by the authorities (especially if the abuse allegations are so far-fetched that no one would belive her). I’m pretty sure that federal marshals aren’t sent halfway around the world simply to arrest murder suspects. (I would expect that they would simply have the Australian authorities arrest her. One might be sent to escort her back to the US but he wouldn’t be the one making the arrest.) So, whatever she is accused of doing is something major enough to justify sending the marshal directly after her and major enough that a wanted poster for her is up in the post office in Australia.
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Kate has mentioned her father before. Yes, it was a brief mention but somehow I think she would have spoken of him differently if she had been abused by him.
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As someone pointed out, a guard posted outside of a hospital room usually indicates that the patient inside is a prisoner; not that they are looking to catch someone coming to visit the patient. Also, the guard who grabbed her outside the MRI room didn’t seem to recognize her (no “got you!” or anything like that) and simply grabbed her because she had contact with her mother. (The police response could have been to the fact that she attacked the guard and took his gun.)
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The license plates and fake ids imply that Kate knows a lot about running and hiding. It seems to be more than what she could have picked up on her own. The experience came from somewhere.
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Kate has also shown herself to be fairly ruthless and manipulative. (Witness the bank robbery in her flashback and how she managed to get Sun to do her dirty work (and take the fall) in this episode. She could “honestly” say to Michael that she didn’t poison him, even though the poison was her idea.) She has consistently manipulated Jack, Sawer and who knows how many others on the island. (Remember the case and how she palmed the key? Jack knew she was up to something by that point.)
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To counter all of this, Kate does have a moral streak (witness her saving the marshal on the flight and the farmer from the wrecked truck). (Though, again, she was perfectly willing to let Jin and/or Michael be poisoned to aid her escape.)
So, given all of this, what did Kate do? Here is my theory…
Suppose Kate’s parents were members former members of some '60s/'70s radical group like the Weathermen or something. They had been involved in a few bombings/bank robberies at some point. Since then they have tried to disapper and have been on the run for decades. Kate is born during this time and this is how she knows so much about survivalism, the fake license plates and so on.
Kate is tired of running and hiding and leaves. She gets involved with someone who turns out to be FBI or something. (Maybe he had been assigned to find her parents, tries to get to them through her and she falls in love with him or something. She may not know what he is until later. (Just for fun, assume the agent in question is the son of the marshal.) This person may or may not be “the man she loved” and may or may not be the person she was briefly married to.)
Kate’s father decides to come out of “retirement” and go unibomber or something. Maybe for a “good” reason; a chemical plant is poisoning the town’s water supply or something. Kate may or may not be involved initally but later does, possibly at the urging of the agent, her boyfriend/husband. (She may know what he is by now and have agreed to help him.) When the plan starts to go down, the agent reveals himself and tries to stop it. It goes bad and there is a shootout. The agent possibly shoots her father and Kate possibly shoots him (maybe he assured her that her father wouldn’t be hurt or something). At any rate, the agent and her father wind up dead and her mother (and anyone else involved) get arrested. Kate escapes, but the only one who knew that she was helping instead of being part of the plot was the agent, and he is dead.
In this scenario, Kate is being persued by the feds because she was involved in a bombing plot and because she killed an undercover agent. This would cause them to send a marshal to Australia after her, explain her behavior and resolve most of the questions above.
Of course, that’s just my theory…
I’m just going off the license plate collection she had in the car. To me, it says that she makes her living using fake ids. If she simply killed her dad and ran away, she could just hole up in a trailer park somewhere. Instead, she is out and about changing her identity as easily as she changes her clothes. That makes her at the very least a grifter.
Interesting thoughts – and good ones (in your post). I had assumed that the guard was there because of the possibility that Kate might show up. But it would throw a totally different angle on things if the parents were already crooked to begin with. And you’re right, it would definitely explain why Kate knows so much about grifting and there would be plenty of possibly scenarios like the one you mentioned. Where perhaps she’s being accused because of the sins of the parents (and yet mom still blaming her for father’s death, assuming he’s dead).
And it would also still be in keeping with the childhood conversation between Tom and Kate (“You always want to run away, Katie”… “Yeah. And you know why.”)
Your theory, or something similar, would make a lot of sense. I like it. 
In TV shows, they also post guards outside hospital rooms to protect the patient. Not so much as a sting operation, but to make sure the attacker doesn’t come back to finish the job.
2): Bank robbery would be a federal crime, no?
4): I thought the “guard” was basic hospital security, and was simply grabbing a person moving rapidly away from the area where a woman is screaming.
5): Not sure I agree.
6): My take on this is that Sun wanted to keep Jin off the raft; asked Kate for help; and Kate suggested making him sick.
The remainder, although fascinating and well thought out, seems implausible as the writers could not possibly present the info and resolve it in any reasonable time span.
This flashback made it pretty clear that she was already on the run from authorities before the bank robbery (I’m sure this flashback was before, due to the plane).
I believe the guard he was referring to was the one sitting outside a patient room when Kate was first heading into the hospital with flowers, not the guard who responded to mom yelling “Help!”
Although I’m with you in that I don’t think it’s that implausible for Kate to have come up with the license plates and on-the-run disguises on her own – I don’t see it as necessarily evidence of some kind of formal training.