There is not a way to move content from one group to another. What you'd need to do is copy the blog post to the new group. You can back-date the post to the original date, and change the author to the original author, however.
When you block a person, they can no longer invite you to a private message or post to your profile wall. Replies and comments they make will be collapsed/hidden by default. Finally, you'll never receive email notifications about content they create or likes they designate for your content.
Note: if you proceed, you will no longer be following .