Can I send messages anonymously if I am not a friend? If I delete him, can he still send me messages?

No, if you post anonymously first, all your friends will be displayed, allowing you to choose who to be anonymous with. If you don’t add him, you can’t post with him. As you said, you deleted him and he is not in your friend list. It would be fine if you are in his friend list. If you have added a friend before and you delete him, but he has not deleted you, he can send you a message. Just block him the next time you send a message!