In Catholic understanding, did Paul speak/write ex cathedra while Peter was serving as Pope? Catholic doctrine teaches that Peter was the first Pope and that Popes may speak "ex cathedra".  When they do, that is considered infallible.

However, while Peter was alive and presumably serving as the first Pope, Paul, John, and James all wrote books that are considered to be Scripture.  In fact, Peter himself refers to Paul's letters as Scripture:


  and regard the patience of our Lord as salvation; just as also our
  beloved brother Paul, according to the wisdom given him, wrote to you,
  16 as also in all his letters, speaking in them of these things, in
  which are some things hard to understand, which the untaught and
  unstable distort, as they do also the rest of the Scriptures, to their
  own destruction.  2 Peter 3:15-16 NAS


Were other people besides the Pope, then, able to speak/write ex cathedra while not serving as Pope?  If so, can others besides the Pope speak/write ex cathedra today?  What is the Catholic understanding of this?
Ex cathedra means from the chair literally. It refers to the power of the reigning Pope to speak infallibly on doctrinal or moral issues. And although, in my understanding, the power of speaking "from the chair" in general is not a concept necessarily new to Catholicism (think of any leader speaking officially from their official seat), in Catholicism it refers specifically to the Pope's authority to make infallible proclamations.

Regarding the letters of Paul, John, and James, we believe that they're inspired writings. But, they're authoritative, per se -- at least not in the same manner of the authority granted by speaking ex cathedra. They're authoritative, if at all, in an unordinary manner. That is, their authority doesn't flow from a natural seat of authority, but from a supernatural infusion of God's grace. I think it's also accurate to say that their authority within the Church flowed from Peter. Their words were binding on Christians only to the extent than Peter bound them.

The authority of speaking ex cathedra, though infused with grace, is an ordinary authority. That is, it is in the nature of the office of Pope to be able to speak ex cathedra. The ability isn't absent until God inspires the Pope to speak ex cathedra; it's always there, regardless of whether the Pope actually is speaking ex cathedra (which is almost never).