What is moral conscience?
Conscience is a court of reason whereby the human person recognizes the moral quality of a concrete act.
As the man know if a particular act is good or bad?
The man knows that a particular act is good or bad by his conscience.
Moral Consciousness can equivocate?
Yes, awareness can equivocate is not well formed, because the front of a concrete act could make a misjudgment against reason and divine law.
How is consciousness?
Conscience is formed with the knowledge of God's law as the Church's Magisterium teaches, with the practice of virtues, prayer, petition the board especially in spiritual direction and frequent reception of the Sacrament of Penance.