One definition is mercy shown to a criminal to reduce a sentence or issue a pardon. For example, if a person has been sentenced to die, in many states the governor may show clemency by reducing the sentence to life.
If it was a felony sentence, no. Clemency is only a 'compassionate' shortening or altering of the sentence, not a forgiveness of the offense.
They can't. And won't. Convicted felons are prohibited from owning (or even "obtaining") a firearm in all 50 states. But if civil rights have been restored (usually by the state governor or a clemecy board), then the person can possibly obtain a firearm legally. But he/she would not need the help of the NRA to do so. One more point about the NRA: convicted felons cannot be members of the NRA.