The only way I know of to “automatically” insert data into a database when a document is uploaded to a SharePoint document library is to write a list event handler. Basically what that will do is fire your custom code whenever a specific list event occurs (ItemAdded, ItemUpdated, etc.). It will be up to the code (which can be VB or C#) to pick off what it needs from the new document/list item and insert that into your DB. I would imagine a simple Response.Redirect() can also be placed in the event handler code which would return the user to the application.
More information on event handlers can be found here. Good luck!

I am considering adding a link to an existing SharePoint site on our application so that users will be able to add documentation to SharePoint ‘from’ our application. After the document is loaded I would like:

(1) To add VB code that will update our application’s DB with the path of the new document so that it can be viewed from our application.

(2) Return the user to our application either immediately, or via a javascript alert. Is this possible?

Thanks.