I live in Manhattan. I love living here!
1. For south of 2k you are at the low end of the market. That would be a very small studio (0br 1ba) in an elevator building, or in a walkup (and 4th+ floor in a no elevator building) *maybe* a 1br 1ba. I live in a 1 br 1ba (~700 sq ft) apartment in an elevator building, and my rent is over $3k/mo - I have a roommate that lives in the living room, we even added walls so there is a room. This type of sharing with temporary walls is a normal situation in NYC apartments. As far as your max budget goes, a lot of buildings require you to make 40-50x the monthly rent, yearly, to even apply to be a rentor.
Be careful when looking at real estate ads, many say "2br" but in the fine print say 1br "convertible". Convertible means, you can add 1 more bedroom if you build temporary walls - converting common space into a bedroom.
Another real estate marketing tactic is the "1st month free" or "x months free" deal. The cost of 1 month's savings is averaged over the term of the lease, and you just pay that small amount less each month. So if you found an apartment for $3000/mo and signed a 1 year lease, with 1 month free, your "net monthly rent" would be $2750/mo. Bottom line: if they are advertising the place with a "months free" deal, ask the realtor what the "net rent" will be.
2. Most rentals in the $2k range only include water and heat. Electricity, cable/internet/phone is all on you. Power in NYC is more expensive then in other parts of the US. My electric bill is over $150 a month, and I just have 1 roommate.
Depending on the area in which you buy, the broker fee structure works differently. In the Financial District (southern tip of Manhattan) listings are usually "NO FEE", which means you do not have to pay a brokers fee - but the building is actually paying it for you. In other areas, there is probably a brokers fee, so imagine it will be about 1 months rent (possibly a few % more). Easy math is you need 1 month rent * 3.5 to move in to a place (1st month rent + security + brokers fee).
One hidden fee that you might encounter is an application fee. When you finally find the apartment that you want, the building may charge a fee (usually between $50 and $100) to process your application to rent the building. Often times on that application you need to submit your financial information.
3. What industry are you in?
4. Same question, it really all depends. It also depends on how awesome your resume really is
5. Totally safe, don't even worry about it. With that said, you can get killed in the safest place in America if you were in the wrong place at the wrong time. Exercise common sense. NYC is a big place, there is a lot of awesome friendly people - but there are also some crazy people and bad apples.
6. Like the other posters have said, there are other places that are more affordable to live in NYC that are outside Manhattan. Come to think of it, I wrote this whole post because it seemed you were interested in moving to Manhattan, but you also refer to it as "NYC". Here is a quick tip: "NYC" refers to all 5 boroughs of New York City (Manhattan, Brooklyn, Queens, Staten Island, Bronx). All of the areas outside of Manhattan have much more affordable housing. Brooklyn for the most part has much better public transit (Subway) then the other outer boroughs. If you do not move into Manhattan (or many parts of Brooklyn), most likely you will want a car.
With all the negative things aside, try to move into Manhattan!!! It's awesome!!! I absolutely love it!!!!