No: Generally, each state has its own bar exams to admit passing candidates to practice law in THAT state. Passing the CA bar allows you to practice law in CA (if you also meet other conditions, like having a regular office there).

Yes: Sometimes a person who is not admitted to practice law in a given state can receive permission to represent another person in one specific case, if he or she is an attorney admitted to practice in another state. This is called a "pro hac vice" admission (informally, "just this once").

Yes again, if the two states have agreed to recognize each other’s bar admissions as equivalent to their own. (Neither NY nor FL recognize CA bar admissions, though.)
References :
- http://www.courts.state.ny.us/ctapps/520rules10.htm – Part 520 – Rules of the Court of Appeals for the Admission of Attorneys and Counselors at Law (New York)
. – http://www.courts.state.ny.us/ctapps/520rules10.htm#10 – § 520.10 "Admission Without Examination"
– http://www.nybarexam.org/ – The New York State Board of Law Examiners
. – http://www.nybarexam.org/AOM/AdmissiononMotion.htm – NY admission by reciprocity (none with CA or FL)

– http://en.wikipedia.org/wiki/Pro_hac_vice
– http://www.courts.state.ny.us/ctapps/520rules10.htm#11 – § 520.11 "Admission Pro Hac Vice" (New York)
– http://www.judiciary.state.nj.us/rules/r1-21.htm – Court Rule 1:21-2. "Appearances Pro Hac Vice" (New Jersey)

Florida does not offer reciprocity to any other state.
References :
http://attorneys.uslegal.com/licensing-of-attorneys/reciprocity/