You can't delete an opinion once you post it its there. Forever, and ever, and ever, and ever. *Fades away for dramatic effect* But, you can change the opinion to anon by clicking the person with the question mark on their face in the bottom right corner of your opinion box.
To go anon before you post your opinion you click the anon check box in the left bottom corner then click "Send It!".
No. Once you have submitted a question, take, opinion, or comment, you cannot edit or delete it. They do not remove posts per user request. If it doesn't violate any site rules, They won't remove it. Please carefully consider what you post before clicking Submit so as to avoid 'post regret'.
However, You can change it to or from anonymous by checking or unchecking the Anonymous box from the post.
And opinion comments can't be added anonymously for the security concerns of the users.