Someone recently also asked what the Pope does. So my answer from there may help with your part of the question on why he has authority.
There is a very good book called:
Why Catholics Do That by Kevin Orlin Johnson.
Chapter 14 is called: The Pope what he does and why it matters
He starts that chapter with the phrase:
"Where you're dealing with a revealed religion like Christianity, you have to be sure that you've got it right."
The short of it is that is the Pope's job, led by the Holy Spirit. We believe that there are times when a Teaching needs clarified and the official interpretation of something needs to be done. While it is true the Holy Spirit works in each believer we have no guarantee that our views are protected from being our personal view in error.
But we do have the promise of that in Scripture for Peter and we believe that is given to his successors as well as the Church in Council in union. The Pope is the first among equals and head of the Bishops of the world. Christ gave the Authority to the 12 and to those who followed them. So Peter's successor inherits his authority. In fact the Pope does not follow or succeed from the Pope before him, we believe each one essentially follows Peter directly so to speak.
In 100AD the Bishop of Antioch (a bishops seat also created by Peter) even wrote in his letters that is the Bishop of Rome who presides over all Christian communities. At the time of course everyone was still unified and Christian meant one thing.
Now, the Pope exercises this power only when speaking "Ex Cathedra" from the Chair of Peter. Which is not common. And he can never introduce new things...he can only clarify what is already in the Tradition passed down by the Apostles or in Scripture. He can not invent.
His job, theologically, is to protect the Deposit of Faith under the guidance of the Holy Spirit when questions arise.
Now, like I said before...we've had bad Popes and none of them have used this authority to change things that could not be changed.
Popes may have disagreed on things, but not on things that are of the unchangeable level.
Ideally the Pope should also be an example of charity, love, virtue, strength and piety. And some have. Some have not.