(Yes, I watched all the videos.)
Do you think the Gospel will change the world?
What degree of change happens at what point in history, is determined by God's sovereignty. The Great Awakening that hit the latter half of the 18th century in Britain, Germany and North America, was a very different world than just before Noah's flood. God decreed those differences.
Should we live under secular laws or biblical laws?
Government is also an institution of God's and I agree with what they said in the first video about different spheres of authority that are played out in the world.
Should secular government be as just, fair and free of corruption as possible? Absolutely. But I also agree that the days of "political theocracy" are over. At least in the terms of what had been instituted in Old Testament times. That whole system was a school master that points all who take note of it to Christ.
So to the degree of an "awakening" of Biblical justice and fairness is present in the civil laws of any given society is indeed dependent on the percentage of that society who are born again. Personally, that is my understanding of "common grace"; not that common grace is an application of the redemption plan. Common grace is simply that society as a whole benefits when rulers rule righteously.
When God uses His church and His people to evangelize and convert people does result in society changing?
Again, redemption is dependent on God's sovereignty and what He determines of percent of the redeemed in any given place in the world at any given time in history.
We are not capable of manufacturing that. And that is where the man-centered concepts of current understanding of Postmillennialism fall. Postmillennialism looks to establish a "golden age" of Christianized secularism just as Israel looks to establish its own "golden age" of Jewish (even global) secularism. (I.E. Jewish rule with Noahide laws etc.) I see both as comparable errors.
The other consideration is that Scripture is pretty clear that Satan is loosed at the end of the millennium "to deceive the nations once again". Jesus poses the question of will He "find faith on the earth" when He returns. That is not indicative of the concepts of Postmillennialism.
Could another (genuine) revival across the world constitute another "great awakening"? That's possible; but if we really are at the end of time, that's not going to happen.