Is there any limit by FAA on the age of aircraft to be operational?
It depends on the aircraft, but in general the answer is that there  are no regulatory age limitations, and indeed we have many aircraft flying that are 50+ years old. 

A notable exception is the Robinson line of piston helicopters. The airframe on those helis is limited to 2200 hours or 12 years, whichever comes first, at which point the entire airframe must be completely overhauled. Some of the airframes are indeed rebuilt, but some are also scrapped, depending on level of wear and corrosion. 

Since the airframe lifetime is in the LIMITATIONS section of the POH, it is governed by:


  § 91.9 Civil aircraft flight manual, marking, and placard
  requirements. (a) Except as provided in paragraph (d) of this section,
  no person may operate a civil aircraft without complying with the
  operating limitations specified in the approved Airplane or Rotorcraft
  Flight Manual, markings, and placards, or as otherwise prescribed by
  the certificating authority of the country of registry.