"The Cleaver of the dawn" means the Creator of the dawn; meaning: the morning when it illuminates. Al-Hasan used to read it as "al-asbah" (the dawns), the plural of "subh" (dawn).
"And He has made the night for stillness" means that creation rests within it. "And the sun and the moon for reckoning."
﴿فالق الإصباح﴾ خَالِقُ الْإِصْبَاحِ؛ يَعْنِي: الصُّبْحَ حِينَ يُضِيءُ وَكَانَ الْحَسَنُ يَقْرَؤُهَا: (الْأَصْبَاحِ) جَمْعُ: صُبْحٍ.
﴿وَجَاعِلُ اللَّيْلِ سَكَنًا﴾ يَسْكُنُ فِيهِ الْخَلْقُ ﴿وَالشَّمْسَ وَالْقَمَرَ حسبانا﴾