Notes requires wifi or cell connection?

Did you “Create an account”, that is, take this step https://doc.e.foundation/create-a-murena-cloud-account ?

If no, you are cloud free.

/e/ does work fine cloud free, but /e/ has been built to be “easy to use” with a cloud, so some of your elementary steps like this one may take a little work / research without the use of murena.io.

There is no easy native backup method. What is in place is still quite experimental [HOWTO] use Seedvault early to understand Android backup.