Not really sure what you're asking...
Administer > Blocks is for moving the blocks around into regions / disabling them, not really for creating content.
You can use the Node as Block module to easily turn your nodes into blocks, and they would still edit it from the content administration section.
Or, you could create a blank block, and in its associated template file (block-whatever.tpl.php) embed the node (node_embed, pretty much what the Node as Block module does) or query for it with a view and embed that (views_embed_view)
Or, if you're using views, you could create a view that queries for the node(s) you want and create a block display for that.
When you're actually building the Drupal site, you should consider what paradigm you're most comfortable with since there are so many ways to get your content together.