Any persistent data would be pushed into persistent volumes to make the containers as stateless as possible. If you look at the upgrade RFC there is a notion to keep the databases outside of Kubernetes to begin with in part to make transition easier.
Can you expand on which connections you mean? By proxy do you mean an HTTP proxy or the smart proxy? By proxy changing files, I assume you mean the smart proxy modifies files on disk. If yes, this is where the smart proxy itself gets tricky and we may have to reduce the scope of actions a smart proxy running in Kubernetes can do vs. one running outside of Kubernetes. I have some thoughts around how to handle the smart proxy I have not shared yet. I will work on getting these available.