Is there any equivalent MySQL UNLOAD?
There are no built-in export functions, but you can easily replicate between two databases via futon (couchdb built-in admin interface).
If you really need a backup as a file, you can "export" all the data through the _all_docs api (see http://wiki.apache.org/couchdb/HTTP_Bulk_Document_API ) but _all_docs does not include attachments - you should get them separately.
Are database files visible using a browser or stored above the root of public_html?
Database files are not accessible from the outside. Why do you need to open them? There is one file in the database, and it can quickly grow to several gigabytes. You do not want to open these files, believe me; -)
Since they are just an add-on, you can safely back up though ...
If the data can be accessed using javascript. How are passwords hidden from the client?
One has nothing to do with the other. Javascript as one of the possible languages for queries is executed on the server, and it would not matter if it were PHP or Java. You don’t need JavaScript on the client at all - you can send your data in plain HTML directly from CouchDB.
How passwords are hidden depends on what you mean: passwords must be provided by the client, and user passwords are stored as a hash in the _users database (but you can also use other authentication mechanisms).
Are there any websites offering couchDB as a standard offer such as MySQL?
You can try CouchDB at http://www.iriscouch.com - they offer free CouchDB hosting.
phpMyAdmin - is there an equivalent for couchDB?
Yes - this is the built-in futon interface. You can reach him through ... / _ utils from your browser. But the interface is completely different - Couch - there is no SQL database ...; -)
Hope I can help!