The basic answer is no. There is no federal registration required, so there is no such thing as a federal registry, and in the few states that do require registration, the average person cannot access the information.
It depends on what you mean. You can obtain some information about the gun itself, such as manufature date by the serial number, but as far as "registration" or finding previous owners or anything...
Serial numbers are required by law to be on the frame (aka receiver) On the Beretta 92, they are located on the left side of the frame, about halfway between the trigger and muzzle. Other models may...