1- when the guard dies due to the “lesser cover” ability on which magic pile does he go to ?
If the guard is your unit he goes right into your magic pile, because he died of his own ability.
2- can he use the ability to absorb more hits than his current health ?
For example when I attack a common unit nearby with 4 dice and I get 4 hits, can he take all those hits instead of the attacked unit ?
Yes, during an attack you first put all the damage onto the attacked unit, and then you check if the damage markers on the unit are equal or higher than it's life points.