Spiritual Milk

In 1 Corinthians Paul makes reference to spiritual milk in his address to those at the Church of Corinth-

1 Corinthians 3:2 - I fed you with milk,not solid food, for you were not ready for it. And even now you are not yet ready, for you are still of the flesh. For while there is jealousy and strife among you, are you not of the flesh and behaving only in a human way?

As I understand it, the Corinthians had received the knowledge of what the Spiritual nature if about, but were not acting in accordance with the Spirit.

So, I have a couple questions -

1. Had the Corinthians not yet received the Holy Spirit?

Or,

2. Was Paul in a sense, acting as mediator between the people and God? Did he have this same authority that we understand Jesus as being the only One who has this authority?

Feel free to explain...