Can you tell when someone regrets their past?

Its usually quite hard. Cos I personally try not to repeat the mistake and never speak of it again. (unless its a really cool story. But that doesn't happen often). Your best chance is to read body language but that could mean risking getting the wrong message.

There is the way that they look into your eyes, or not. There is also the factor of their willingness to make things right from when they did whatever it was that was wrong. You can also tell by the way that they try to not repeat their mistake from the past.

That said, I is also hard to tell if a person truly has changed. If it is an abusive guy, they are statistically (and by common sense) likely to continue their abusiveness. Other things are a little easier to change, and they're more likely to be the truly regretful, or to use a better word, repentant.

Yes, if they no longer act that way in the present!

If they are no longer like that, chances are they do regret it. Everyone makes mistakes in their life that they wish they had not made. Just be careful of people that say they regret how they were in the past, but continue to make the same mistakes. Those people do not truly regret their old lifestyle, otherwise they would not still be doing it.