Personality belief: The word Anatta basically means that there is no permanent personality, permanent entity. As long as we believe there is something here then we cannot become enlightened. By definition, when a person penetrates the understanding that there really is no permanent identity here, no permanent personality, then if they penetrate only momentarily, then they become a Stream-Enterer. By definition, at the first level enlightenment they can forget it, they have it in their mind for a little while. They can forget it, they can remember it, they can forget it, it's not permanent. The personality belief does not fully vanish at that level. It does not fully vanish until the person is fully enlightened, called an Arahant. As I understand, that's the only time it permanently vanishes.
I'll give you the story about Anuruddha. Anuruddha was a cousin of the Buddha. He was a very gifted man; when he heard the Buddha teach, he immediately became a monk early in the Buddha's teaching period. Within a very quick time Anuruddha became a non-returner (that's the third level enlightenment). He became a non-returner and as he did, he also developed the psychic ability to see back in time as far as the Buddha. He didn't have all of the physic abilities to those of the Buddha, but in this particular one, he even matched the Buddha. He was equal to the Buddha in the ability to see back in time.
After more practice trying to finish the job, trying to become fully enlightened, he couldn't. He just couldn't get fully enlightened, he was stuck on the third level. He was trying very hard to get fully enlightened, but he couldn't, and he didn't know why. So he went to Sariputta who was the most gifted, enlightened disciple of the Buddha on the wisdom level. He didn't have that much psychic ability, but he had a wisdom level the highest of anyone except the Buddha. So Anuruddha felt that maybe Sariputta could help him.
He went to Sariputta and said "Sariputta, can you help me? Here I am, I'm a non-returner, third level enlightenment, and I have the psychic ability to see back in time as far as the Buddha. But I can't get fully enlightened yet, even though I have this psychic ability. I can match the Buddha on psychic ability, I still can't get fully enlightened. Can you please tell me sir, why is it that I can't get fully enlightened even though I'm a non-returner and I have this ability". Sariputta said, "You're too conceited."
Anuruddha was holding onto "me", I have this ability. He had a personality belief that he, he,, himself, has something and that was blocking him, even though he was a non-returner, the third highest level. So the personality belief at this level does not fully vanish, but of course it would be gone much more than on the lower two levels.
As to being free from attachment to the eight worldly dhammas, well no, none of the bottom three levels are totally free. Because here we have the story of Anuruddha who was attached to his psychic ability, to his gain, to his fame, to his status and so on. So he was attached, even though it would have been very subtle on this level, he still had this attachment so the eight worldly dhammas. Attachments can still be there for anyone unless they're fully enlightened.
As to the ending of the question concerning the eight worldly dhamma section of the question: Would there be some concern about what other people think of them? Okay, now to a large degree we don't have to wait until we are a non-returner, we don't have to wait until we're a stream enterer, the first level, before we work very hard trying to not care what other people think of us. It's possible for people who aren't so enlightened to not really care what other people think of them. These are the people who are more selfless in their life. For example someone like Mother Teresa, who would get blamed and criticized by other people and she would say, "Oh, too bad". She didn't care. There are just human beings who aren't even partly enlightened and can let go of the eight worldly attachments a great deal, so you don't have to wait.