Yes, you are describing a hosted instance. Masto.host looks good, and the cheapest option is only $6/month. The problem with this federated approach is that the actual federation features can become pretty expensive. Hosting is cheap but if you have thousands of followers from different instances federation processes will become very expensive.
As far as I know, this is all cached at an instance level. So only the first person to pull something from your instance actually hits your instance's resources. I can still see posts and users from dead instances because it's all cached on my instance. There's a rake task to wipe it, but people are advised not to since those caches have been what saved at least one instance whose name I can't remember.
