R&S - I know there will be non-members on the earth during the millennium. In Mormon Doctrine starting on page 498, it explains that honest and upright people will not have their free agency taken away, "They will continue to believe their false doctrine until they voluntarily elect to receive gospel light."
My questions are...

1) I assume these non members can continue to attend their own churches as well? The actual buildings they worship in will still exist during the millennium?

2) Will there still be a Pope and other high ranking leaders of other churches during the millennium?

JOEL - As far I know the answer to both questions is, yes, but they will all eventually acknowledge Christ's kingdom and government. Here are some things Brigham Young said:

"When all nations are so subdued to Jesus that every knee shall bow and every tongue shall confess, there will still be millions on the earth who will not believe in him; but they will be obliged to acknowledge his kingly government".(Discourses of Brigham Young p. 115)

"The order of society will be as it is when Christ comes to reign a thousand years; there will be every sort of sect and party, and every individual following what he supposes to be the best in religion, and in everything else, similar to what it is now." (Brigham Young, JD 2:316.)

"In the millennium men will have the privilege of being Presbyterians, Methodists or Infidels, but they will not have the privilege of treating the name and character of Deity as they have done heretofore. No, but every knee shall bow and every tongue confess to the glory of God the Father that Jesus is the Christ." (Brigham Young, JD 12:274.)

If those other religions still exist then most likely their leaders will also continue to function until they are no longer needed, because as President Joseph Fielding Smith said:

"The gospel will be taught "far more intensely and with greater power during the millennium, until all the inhabitants of the earth shall embrace it. . . . Through the revelations given to the prophets, we learn that during the reign of Jesus Christ for a thousand years eventually all people will embrace the truth." (Joseph Fielding Smith, Doctrines of Salvation, 3:64.)