All blogs are independent sites so what you do on or with one has no affect on any others.
To delete a free hosted WordPress.COM blog you must be logged in under the exact same username account that registered the blog. To prevent accidental or inadvertent deletion of blogs, there are multiple warnings given that blog deletion is permanent and irreversible. Lastly, a verification link is sent in an email and must be clicked to delete a blog. If clicking that link does not work then copy and paste it into your upper browser window and click. http://en.support.wordpress.com/delete-site/
Deleted blog URLs are not recycled, regardless of who registered and deleted them and no exceptions are made. http://en.support.wordpress.com/recycling-blog-names/