The process of saving a running instance to S3 is called "bundling" in Amazon terminology.
While this method of bundling server images is supported in the Dashboard, our preferred design approach is to create a server template, which is a base AMI image that you can customize by adding RightScripts. It's a much easier way to manage servers and you also avoid a bundling version nightmare. But, if you're comfortable with your bundling process you could always get something up and running and then migrate to a server template solution at a later time.
If you wish to bundle a running instance in the Dashbaord, click on the Nickname of a running instance.
Click on the Bundle button.

Bundling a running instance will save a copy of your server's image to S3, which you can later use for rebooting a server. Bundling a server does NOT "hibernate" or "suspend" the image; the instance will remain operational. You are only taking a snapshot of it at that particular time.

You raise an interesting question. At the current time, we recommend unmounting an EBS volume before bundling an instance. The mount point should be left intact but, the volume should be "not mounted" before bundling an instance. We realize this is not the most graceful way, but it should work for now. In the maintime, we're working on a better solution for this type of scenario. Thanks for your comment!
-Dean