By default, it seems that SharePoint cannot execute a Workflow if an Anonymous user is creating a item.
Can someone help me on this?
Since the process (workflow) runs as the user that created the item, this does not work for anonymous users. There are some settings to enable this for content that is emailed in to the library, but for this work for regular items you would need to find a way to kick off the workflow and impersonate another identity. You could potentially initiate this with a timer job or event receiver.