If a person abandons a sin without remorse, is his repentance considered valid? And how does one resolve not to return to the sin, by utterance or by the heart?

Repentance from sin has pillars: abandoning it, regretting having committed it (which is the greatest pillar), and resolving not to return to it. If the disobedience relates to the right of a human being, then it has a fourth pillar, which is seeking absolution from the owner of the right. So, whoever does not regret the sin, their repentance is incomplete. The resolve to abandon disobedience is in the heart and does not require verbal utterance.