Q: Am I allowed to fly a N-registered aircraft using my JAA license?
A: Yes, in accordance with FAR 61.3 (a)(1) you are allowed to operate an N-reg aircraft using a pilot license issued in that country subject to that country laws and regulations. For international flight however, you are required to hold a FAA pilot certificate
Q: I obtained a FAA PPL based on my UK/JAA/EASA license recently, can I now fly a N-Reg aircraft?
A: You need to have completed a flight review within the last 24 calendar months as required by FAR 61.56 and meet the applicable currency requirements of FAR part 61 for your type of operation (ie you might require additional endorsements for complex, tailwheel, pressurized and high performance aircraft (>200hp)
Also you need to meet the applicable validity and currency requirements of your UK/JAA/EASA license and have a current medical.
You are also required to hold a FCC radio license for any international flight outside the USA, a step-by-step guide is found here
Q: I have a FAA PPL based on my UK/JAA/EASA license. Do I require a FAA medical?
A: You are exempt from holding a FAA medical certificate if you hold a current medical certificate issued by the country of your foreign based certificate FAR 61.3 (c)(2)
Q: What are the advantages of obtaining a full PPL rather than operating on the foreign based FAA pilot certificate?
A:
Q: What is a FAA flight review and what does it include?
A: A flight review as per FAR 61.56 normally consists of 1 hour of flight and 1 hour ground training given by a FAA flight instructor (CFI). It normally consists of a review of the FAA rules and regulations of FAR Part 91 and review of the maneuvers/operations deemed necessary by the Flight Instructor giving the review. After succesful completion the FAA flight instructor endorses the applicant logbook which is valid for 24 months.