Utopian is an app that accesses the Steem Blockchain, so it is independent of Steemit - but posts made using Utopian will also appear in Steemit since Steemit looks at the same Blockchain. It's just like how Dtube works.
You can sign in to Utopian using your Active Key from your Steemit Permisions Page.

I don't know all the details of the problems with Steemit because I don't have access to the server logs and Steemit Inc. are not being transparent regarding the problems being faced. :/