He seems to be moving on with his life and completely forgot about me. Do they regret losing people who loved them? Do they ever realize their faults and mistakes eventually? 

Narcissists regret losing supply. They don’t care about true love other than how it serves them. If you love them, you will do a lot for them, so they regret losing the supply they get from loved ones. But they find new supply, new people to believe their lies, cater to them and put up with their BS. They do not understand or are able to offer you true love or a healthy relationship. Everything, both good and bad, is about gaining some sort of supply.

If they lose a good supply, they will find that as a fault, but it’s of little to no concern on how they hurt you. If they cheated, they may regret getting caught and improve their skills, but your broken heart isn’t going to make them shed tears. They shed tears for only themselves. 

So, breaking your heart, cheating on you, not validating your feelings, take advantage of a good person they are not going to regret. Losing control of you, you finding out the truth when they didn’t want you to, those are things they will regret. This is part of the disorder, a lack of empathy. They simply do not see life or partnerships the way you do.