Here are some excerpts from FAA Order 8130-2D covering the your questions. Full text of this document can be found at:
http://av-info.faa.gov/dst/reference.htm#Orders
CHAPTER 7. SPECIAL FLIGHT AUTHORIZATIONS FOR NON-U.S.-REGISTERED
CIVIL AIRCRAFT
224. GENERAL.
a. The navigation of non-U.S. registered civil aircraft in the United States is permitted under
§ 41703(a) of Title 49. This section is implemented by 14 CFR part 375, Navigation of Foreign Civil Aircraft Within the United States (part 375), which sets forth the rules, conditions, and limitations governing the navigation of non-U.S. civil aircraft in the United States. Part 375 also specifies that non-U.S. civil aircraft being operated in the United States shall carry a current and effective AIRWORTHINESS and REGISTRATION certificate issued or rendered valid by the country of registry.
Part 375 also allows the operation in U.S. airspace, subject in some cases to prior DOT
approval, of aircraft that do not carry current airworthiness certificates, but that have been issued an SFA by the FAA.
a. General. Section 91.715 is applicable to a non-U.S. civil aircraft which DOES NOT have a
current airworthiness certificate or equivalent to a U.S. standard airworthiness certificate, which
indicates that the aircraft complies with a detailed and comprehensive airworthiness code as provided by ICAO Annex 8. An SFA is required for an aircraft carrying an airworthiness certificate, flight permit, or similar document issued by the country of registry that is equivalent to a U.S. special airworthiness certificate. See 14 CFR § 375.10, Certain Foreign Civil Aircraft Registered in ICAO Member States, for details concerning aircraft manufactured in a country prior to that country becoming a member of ICAO.
b. Individual Aircraft Authorizations. An application for an SFA should contain the following
information, as applicable, and any other information deemed appropriate by the cognizant FAA field office.
(1) The name and address of the applicant, if different from that of the registered owner. If the
applicant is not the registered owner, a letter from the owner appointing the applicant as agent will also be submitted.
(2) The name and address of the registered owner of the aircraft.
(3) The operating purpose for which the SFA is requested.
(4) The type of airworthiness document, if any, issued for the aircraft by the country of
registry.
(5) Information such as total aircraft time, maintenance status, date of last inspection, type of
inspection, and the name and title of the person performing the inspection. This information is
necessary to establish that the requested flight(s) will not adversely affect safety.
(6) The make, model, and serial number of the aircraft.
(7) The assigned non-U.S. nationality and registration marks, and a valid copy of the
registration document issued by the country of registry and translated into the English language.
(8) The base of operations for the proposed flights and the areas where the flights will be
conducted.
(9) The proposed U.S. port of entry and the itinerary while operating in the United States.
(10) For aircraft being exported, the route to the U.S. border and ultimate destination.
(11) Whether the aircraft is to be modified in accordance with FAA-approved STC data, and
will require maintenance flight testing in the U.S.
(12) Whether the aircraft will be used as a "test aircraft" in the development of a U.S. STC,
and will require flight testing for the purpose of "showing compliance with the regulations."
(13) If a damaged aircraft is involved, the operating limitations, if any, assigned by the country
of registry after its inspection.
(14) The duration for which the SFA is requested.
(3) Ferrying an Aircraft for Export Delivery.
(a) Individual Aircraft Authorizations. All the minimum operating limitations should be pre-scribed for an aircraft operated for this purpose except that the limitations under paragraphs 230a(4), (7), (8), and (9) of this order may be omitted if the aircraft has a valid Form 8130-4 with no major exceptions listed, and/or is not carrying extra fuel or navigational equipment. If temporary fuel system(s)/equipment are installed and/or the aircraft is to be operated in excess of its maximum certificated takeoff weight, the limitations in para-graph 175 of this order should be included as applicable. The following special limitations should be applied in all cases:
1. Permission for flights over or into countries other than the United States must be obtained
by the owner or operator of the aircraft from the CAA of that country.
2. The aircraft shall be flown to the United States border from the point of departure by the
most direct route not in conflict with other operating conditions and limitations of this authorization.
3. The aircraft shall not be operated with temporary fuel system(s) or temporary navigation
equipment installed, or at a weight in excess of its maximum certificated takeoff weight, unless approved by the CAA of the country of registry in writing.