These are great sentences and in general they are correct. I will say one thing... In the examples, you use the past simple (weren't proud of/were ashamed of/regretted). If now you are still not proud/are ashamed/regret, then use the present simple to show you continue to feel this way.
We have all done things we weren't proud of (in the past, we were not proud)
We have all done things we aren't proud of (and we continue today to not be proud)