None. As probably the greatest racehorse of all time, Secretariat produced no Triple Crown winners himself. Some of his offspring did well on the track, but Big Red was more a producer of exceptional fillies that grew up to be broodmares that produced many winners.
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Several.Among the best were: Risen Star, winner of the Preakness and Belmont in '88.
Terlingua, winner of 7 grade one stakes as a filly.
Lady's Secret, horse of the year in '86, Distaff winner.
General Assembly, winner of several grade one stakes.
He had 653 foals.
From what I've read and seen in the new movie, he has sired more than 600 foals through out his time
Many, but most notably, sons Risen Star, General Assembly, daughter Lady's Secret.