Can a Sport Pilot CFI give a flight review to a Private Pilot (and sign off)?
Interesting question. 14 CFR 61.413 says a Sport Pilot Instructor is authorized to give the training and endorsement for "A flight review or operating privilege for a sport pilot." This could be interpreted in a couple of different ways, including only to someone who holds no more than a Sport Pilot certificate or to someone exercising only sport pilot privileges. It isn't clear, and there are no Chief Counsel interpretations on point. But it wouldn't make sense to say a CFI-SP can give a flight review to a Sport Pilot in an LSA but not to a Private Pilot exercising Sport Pilot privileges in an LSA. So, absent any guidance from the FAA, I'd say "Only in a light sport aircraft in which you hold pilot and instructor privileges and in which the reviewee is rated, and only if the flight is conducted within the limitations of a Sport Pilot (e.g., not at night)."