As for the Sandbox and data management, typically the data is migrated directly to the Production environment. First though all your config and testing can be (is) done in the Sandbox(es), which can be transported to Production. I don't think the data itself is transportable.
I wouldn't say the sandbox data is on a different server, but it is separate from your production data with different record IDs, etc.
If you're migrating data from another system, you could certainly do a dry run of that import into Sandbox, to make sure everything works as planed, and the re-do your import into Production. AFAIK there's not an easy way to migrate data from Sandbox to Production.
What you can migrate easily from SB to PD is customizations and configurations, like new fields, new objects, Apex triggers, Visualforce pages, and so on. That way you can build and test new features in SB, then deploy them to PD.
Finally, a Developer account is a free, standalone account that is more like a Sandbox, but it's not easily possible to mirror your Production configuration into a Developer account. With Sandbox, when you refresh a Sandbox, it copies your entire configuration (all your custom everything) from Production and makes an exact copy of your org in Sandbox. Developer accounts start from scratch, without your customizations. You can certainly migrate customizations from Developer to Production.
Does that answer some of your questions? Clear as mud? Let me know, I'm happy to clarify anything that doesn't make sense in there.
Quick question, how big is your admin / development team? Bigger organizations tend to use Developer accounts as a standalone environment for individual developers, so they aren't stepping on each other's toes, and then they migrate to Sandbox / Production from there. If your team is smaller, it might make sense to just work with the Sandbox.