Questions about the Catholic faith

A young gentleman of my acquaintance has asked me several questions about my faith.  They are serious questions, and they deserve thoughtful consideration.

I am Catholic.  He is a member of the Reformed Presbyterian Church.  He lent my family a book, The Five Points of Calvinism, to explain some of his faith.

In asking his questions, he did clarify to say that when he asks what I believe, he is asking what the Church teaches.  I should state at the outset that I'll do my best, but that I am imperfectly catechized at best.  I plan to refer to the Bible and the Catechism, as well as to some sites and publications that I feel comfortable with.  If anything I write raises an eyebrow, please ask about it in the comments and, of course, feel free to research it yourself.  I don't hold myself out as an authority; I'm just doing my best.

In attempting to answer his questions, I will need to distinguish between explaining and defending my faith.  Explanations will refer to sources I accept but that he may not accept.  When I attempt to defend, I will try to refer to sources that both he and I accept.

As I told him once, I imagine that if we sat down side by side and started quite at the beginning ("In the beginning God created heaven, and earth...") and moved forward from there, 95% of our beliefs would be congruent.

Here are some of his questions:

"Mary- Do you believe she is perfect? Did she stay a virgin or have other children? Do you believe that she should be prayed to?"

"The Pope- Do you believe when he is speaking from the “chair” that his words are without fault? If so, how would you explain that?"

"Do you view Priests as mediators between us and God? Or is Christ the only one who can fill that role?"

"Do you believe that our faith is justified only by Gods grace or are works a part of that justification? I understand that “By our works shall we be known” but are those works saving works or just the fruit of being saved?"

Shortly, I'll work on addressing them as best I can.