Yes.
Yes, absolutely. But, it's only legal if you have a New York permit. As I understand it, New York state issues a permit, but New York city issues its own permit and does not recognize state issued permits.
The fee for a New York State learner's permit is $80.
no
no
"Permit" ... to do what? If you're talking about a driver's license (or learner's permit), you should contact the New York DMV. I can't tell you a price because I have no idea what kind of permit you're talking about.
80 dollars, but you pay for it all when you get your permit
Yes, with restrictions. While you may operate a motor vehicle in New York State on an out-of-state learner's permit, you will be subject to the restrictions imposed on permits both by the State of New York and the state issuing the permit (in this case, Florida). Additionally, the State of New York does not allow an out-of-state permit holder to drive in New York City.
No.
yes
Yes.
A learner's permit is valid for 18 months.
No, you can only drive in New York with a valid licence.