for a time, then realize the lesson to be learned from the mistake and consider it something you made to learn better from, and never repeat again. that is the trick to forgiving yourself for a mistake. not repeating it and learning from it!
Yes, there are things we SHOULD regret, can we change them, no. Best thing is to not dwell on them but to learn from our mistakes.
Yes. It puts us on the road to better choices.
I like nr75's answer. Don't you?
It's better to regret something you have done, than regret something you haven't.
Not my quote, but one of the many little maxims I live by.