1)
Why does it mention giving "Chukim" and "Mishpatim"?
1.
Malbim: Chukim are to fix man's matters pertaining Bein Adam la'Makom. Most are of the Nefesh and are tied to Elokim. Therefore, their reasons are not known. Mishpatim are for Bein Adam l'Chavero. They have a reason. Most are based on man's physicality, and he lives in society. Man must do both, for he is a composite of body and Neshamah.
2)
To which life does "va'Chai Bahem" refer?
1.
Radak citing Targum Yonasan: Life in the world to come. And so is Targum Onkelos of "va'Chai Bahem Ani Hashem" (Vayikra 18:5).
2.
Malbim: It refers to physical and spiritual life.
