Regarding not being able to delete posts. In short, Q2A will not allow you to delete posts that have children posts. E.G.: you wont be able to delete a question that has comments or answers and you won't be able to delete answers that have posts. So first you'll have to delete all children and then you should be able to delete the post itself. Ami has written a plugin to overcome this limitation that would allow you to delete all posts and their children. I've never tested it but I guess it works fine: https://github.com/amiyasahu/q2a-delete-hidden-posts
Regarding anonymous users posting questions, answers and comments. I think no "only registered users can post a question" setting exists. You can configure this in the admin/permissions section of the site. The options are called "Asking questions", "Answering questions" and "Adding comments". Just make sure to set them to "Registered users with email confirmed". Alternatively, you can set it to "Registered & email confirmed & enough points". That way they will have to play with the site for a while before posting (e.g.: casting votes) which will make the process harder for spammers and hopefully they will give up.