I don’t understand. Are you running hassos or using a venv? If hassos, you are not supposed to install anything inside the container, that is not how docker works.
About your first question : that is normal behavior. Anything added this way to the container does not ‘stick’, that is normal docker behavior. You are not supposed to install anything inside the container.
You don’t. The image always comes with the correct version of pip and python for that version of HA. If a new version of pip or python is needed, the dev’s will build it in the new container when a new version of HA arrives.