The best place to start answering your questions is the New York City Department of Parks and Recreation Special Event FAQ.
When thinking about your event, you should know that all events in the City of New York with more than 20 people attending will require special event permits. Please fill out the event application form and fax to: Citywide Special Events, Fax: (212) 360-1478.
There is $25 non-refundable administrative processing fee for all special events permits.
People who want to sell at, charge for, or conduct any sort of revenue-generating activity on parkland for a short period of time should read the Temporary Use Authorization (TUA) Guidelines (16 kb).
More information about special events in Central Park can be found here:
Citywide Special Events voicemail information:
(212) 360-1319, or (212)-408-0226