my understanding is that terms of service would be helpful but not needed if someone trued to sue because you blocked access to the site. I would not expect ToS for a site like you are explaining, but if it did it would say "the web admin will ban you if you are naughty, you have been warned"
For privacy policy i think what you wrote to give us context is near perfect. Explain how your app stores data, be specific about encryption at rest and in motion. If your app is designed to hold name, email address, billing info you should highlight that in your policy. including a (monitored) contact email for questions would be nice, but not needed imo unless you are storing PII