1) How much should I pay if I want rent an apartment in a good area.
Apartment rental will vary alot depending on the area/size/quality of apartment. There are lots of good areas. To get a feel have a look at the streeteasy website for rentals:
StreetEasy: NYC Rentals, Manhattan Apartments & Rentals In New York City, Brooklyn, Queens And The Bronx
to get an idea of costs in different areas.
Also New York magazine website gives a good overview of the areas:
2) how much is the normal utility bill
Normal will be different for different people, but for us in a one bedroom apartment with no airconditioning and 1 person working from home - gas = $20-$30 per month, electricity = $50-$70 a month, heat and hot water are provided by the building. Cable/internet/phone - depends on what you get, but basic cable and internet is about $90 a month
3) how much is the food expense
Again depends on what you eat/how much you eat/how often you eat out etc, check out my blog - a little big apple - i have talked a bit about grocery shopping and cost. For us, we spend about $80 (for 2) a week on groceries (once you have all the basics in your cupboard)
4) and is it very difficult to apply for a job there?
We are going through this process at the moment, trying to find my husband a job as he has almost finished his masters. Everyone keeps telling me it is all about networking, meeting someone, who knows someone, who has a job for you etc.