1. The 'Reconquista' was the RECOVERY of Spain from Muslim aggression centuries earlier. It was a centuries-long process that was completed at the end of the 15th century.
2. The 'violent' activities of the Conquistadors was NOT condoned by the Church, either in Spain or in Rome. In fact, Catholic missions repeatedly COMPLAINED about the harsh treatment of the natives; complaints that led to the ending of the encomienda system in the 1540s.