First, some background to this psalm. According to the Cambridge Bible this psalm was composed by an author who lived in Jerusalem during times of crisis yet survived miraculously:
These Psalms cannot be merely general expressions of confidence in
Jehovah as the protector of Zion. They plainly owe their origin to
some definite historical event. The Psalmist writes as the
representative of those who have recently passed through some terrible
crisis of anxiety, who have seen with their own eyes a signal
manifestation of God’s power on behalf of His people, comparable to
His mighty works of old time, and who have recognised in the course of
events the proof not only of Jehovah’s love for His own people but of
His universal sovereignty.
What that deliverance was is anyone's guess, but it goes on to suggest a few possible victories of Israel over its enemies that would've prompted this author to compose this psalm:
- victory over Sannacherib and the Assyrian army.
- victory of Jehoshapat over the Ammonite and Moabite army. (commentary by K&D)
- victory of Ahaz against Rezin and Pekah.
Whichever victory it was that prompted the psalmist to write this, the aim of this composition is to show that Yahweh is supreme and victorious over the pagan gods, that "he breaks the bow and consigns wagons/chariots to the flames" (verse 9) according to his will, and no one can stop him. That he loves the city of Jerusalem and dwells in her midst and the city can never be toppled (verse 5). Then in verse 10 the author goes on to address the nations of the earth; that is the enemy who attempted to conquer the "city of god" and destroy its nation as well as the other enemies of Israel,
Desist! Realize that I'm God!
I dominate the nations;
I dominate the
earth. (NJPS)
The translation by the NIV, "Be still", doesn't do justice to the text. The more appropriate translation is "Desist!", as the NJPS has it. The root of this Hebrew word, h-r-f, is the same root used in Deut. 9:14 to denote a halt or discontinuation, "Let me alone, so that I may destroy them." Here too it is a call to halt and desist from war. The psalmist calls upon (or warns them) the nations of the earth to desist from attacking Israel again, because Yahweh is supreme and cannot be overcome. He is the "Lord of Hosts" and will always protect his nation and his city Jerusalem.
So to answer your second question, "What does "be still" denote? My answer is, an absence of activity to the enemies of Israel as I explained above. As for your first question I will not attempt an answer in this post (it is in nature more philosophical than hermeneutical which is beyond the scope of this answer).
Hope you find this helpful.