To answer your questions:
(1) Yes, your chances are basically zero with that score given your profile. You realistically need a 700 or above.
(2) The biggest concern is that you risk coming across as one dimensional and narrow minded. From what you wrote, the adcom will wonder whether you can talk about anything outside of finance, because you've been all finance all the time (and even a business undergrad no less). This can be a huge concern as you will be working with your fellow classmates who are from a variety of professional backgrounds and seeking all kinds of post-MBA careers.
(3) Shoot for 700 on the GMAT. Beyond that, it's choosing a range of schools that are a better fit for you, and then doing the best you can on the applications. You are who you are and you can't change that in a matter of weeks - so all you can do is focus on the application itself (GMAT, essays, rec letters, interviews, etc).
(4) Assuming you do reasonably well on the GMAT (700+ ideally, 680+ minimum), Columbia, Chicago, INSEAD, and LBS are stretches - choose two or three from this list. NYU, Yale, Cornell are sweet spots that are likely better suited for you (and where you will have a better shot of getting in).
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