"Trust in the Lord forever, for the Lord, the Lord himself, is the Rock eternal." NIV translation
This "perfect peace" is only possible through Jesus Christ as he is the Rock that is mentioned here.
A rock is not describing some little boulder that can easily be moved but speaks of something that is very large and immovable. We can have this peace by remembering how Jesus has brought us through the tough times and especially by remembering that He has never left us or forsaken us.
"He humbles those who dwell on high, he lays the lofty city low; he levels it to the ground and casts it down to the dust. Feet trample it down - the feet of the oppressed, the footsteps of the poor." NIV translation
The phrase "those who dwell on high" speaks of the proud and we are reminded of the fact that pride is a characteristic of the devil. The lofty city speaks of the chief city of the new world order that is set up to oppose God during the Great Tribulation.
The song celebrates the fact that God has destroyed that religious system and the city that was at its center. The poor and oppressed refers to those that have understood that they could not achieve salvation on their own and have accepted the grace of Jesus Christ.
During the Millennial Reign, people will rejoice at the replacement of religion with a restored relationship between God and men.
"The path of the righteous is level; you, the Upright One, make the way of the righteous smooth." NIV translation
The path speaks of faith in the completed work of salvation through Jesus Christ. This path is so simple (level) that it has been a stumbling block to the religious. Since the fall of man, he has this inherent desire to work to achieve something and that is the basis for most "religious activity". The path of any religion seems like an uphill climb as men must constantly work to achieve their goal. Through Jesus Christ, our way to achieve salvation is like a nice stroll on flat ground. We simply accept His gift and trust in what He has done on our behalf.