According to premillennialism, are the nations in the New Earth still procreating?

Robertson's Word Pictures addresses your question:

"Maketh an abomination and a lie (poiōn bdelugma kai pseudos). Like Babylon (Rev_17:4 which see for bdelugma) and Rev_21:8 for those in the lake of fire and brimstone, and Rev_22:15 for “every one loving and doing a lie.” These recurrent glimpses of pagan life on earth and of hell in contrast to heaven in this picture raise the question already mentioned whether John is just running parallel pictures of heaven and hell after the judgment or whether, as Charles says: “The unclean and the abominable and the liars are still on earth, but, though the gates are open day and night, they cannot enter.” In apocalyptic writing literalism and chronology cannot be insisted on as in ordinary books. The series of panoramas continue to the end."

I would add the caution not to be sidetracked by seeing one's name in the Book of Life as irrevocable: Revelation 3:5 and Exodus 32:33 indicate it is not.

I often ponder how Satan could fall.

Apparently children will still be born there: Isa 65:17

For, behold, I create new heavens and a new earth: and the former shall not be remembered, nor come into mind. 18 But be ye glad and rejoice for ever in that which I create: for, behold, I create Jerusalem a rejoicing, and her people a joy. 19 And I will rejoice in Jerusalem, and joy in my people: and the voice of weeping shall be no more heard in her, nor the voice of crying. 20 There shall be no more thence an infant of days, nor an old man that hath not filled his days: for the child shall die an hundred years old; but the sinner being an hundred years old shall be accursed. 21 And they shall build houses, and inhabit them; and they shall plant vineyards, and eat the fruit of them.

I wonder if the whole purpose of human finite lives on Earth since Adam's Fall, during which our knowledge is limited and God's presence is, in the words of Matthew 25, as it were "in a far country", has been to give us a chance to make our choice between God and Darkness a habit able to endure throughout eternity, so that never again after Satan's fall would any soul enter Heaven and later decide to leave. In any case while on this Earth Hebrews 6 assures us of the possibility of falling for even the most spiritual of humans who do not "watch", as Jesus warned; and Isaiah certifies that there will still be "sinners", even in the New Earth, in which people do not yet live forever.

Could it be the New Earth is a chance for fence walkers in earlier ages, whose goal was the minimum requirements for their ticket to Heaven, to get one more chance to finally make up their minds?

In the historicist framework of Ellis Skolfield, Christ returns at the last trumpet (the seventh trumpet) and the time of the new Earth is immediately ushered in. The righteous receive their new bodies, while the damned are immediately dispatched to Hell. No one from this time forward has any children. In Matthew 22:29-30 it says:

Jesus replied, “You are in error because you do not know the Scriptures or the power of God. At the resurrection people will neither marry nor be given in marriage; they will be like the angels in heaven.

According to Skolfield, the tribulation and the millennial reign of Christ coexist simultaneously. Thus we are currently in the midst of the tribulation, and we are also in the Kingdom of God, because Christ ascended to the throne about 2,000 years ago.

As for the length of the time periods, he argues that the word for millennium used in the Greek, chillioi, is an indefinite plural, hence can refer to multiple thousands of years.

As for the time when the nations will once again be deceived, he argues that over the course of the last century, especially since the founding of Israel, many nations (faithful or not) that once gave lip service to Christ being their ultimate sovereign have since abandoned even the pretense of following him.

Adding another answer as it is substantially different from my first answer.

There is a viewpoint irrespective of millennial position, that the city in this passage is a symbolic representation of the church, and not a literal city. Taking this symbolic viewpoint, verse 27 would simply be saying that no one unclean enters the church, which in turn simply implies that people must be cleansed first, which implies a connection between "having been cleansed" and "written in the Lamb's book of life".