It ll be tight, but it should be possible. I d recommend going for an apartment with a roommate. I think you can get your own room in a nice apartment in a nice neighborhood, for around $700-800.I d suggest an area like Kensington - good area, pretty safe, very diverse, right near trains and prospect park!
No shot...living (in general) in NYC is expensive. Rent alone can knee cap you--especially on minimum wage. Even a 1 bedroom apartment in a crappy neighborhood can be a pretty penny. I strongly advise not to do it
Possibly, but you would most likely not enjoy the neighborhood. There are some dangerous places in B Klyn...
Absolutely not. Your going to have to get another job at least, or find a few really savvy roommates.
Not unless you go on welfare and live in the ghetto. I know people do live that way but its not very good.