How can I repent from committing Zina with my cousin, and is my repentance only from the heart? How can I know that Allah has forgiven and pardoned me, and is there any expiation or prescribed punishment for this?

Adultery is a grave sin, and its sinfulness is compounded if committed with a relative, as it then includes the breaking of kinship ties. Sincere repentance (tawbah (definition) nasuh) is obligatory and expiates the sin. One should not be lenient in interacting with non-mahram (definition) women to avoid falling into immorality again. Among the signs of accepted repentance are an improved state of being thereafter and an increased devotion to acts of obedience.