I don't believe that LV has a direct link to Determination, so correct me if I'm wrong, but...
Also, possible spoilers, just cuz there is some stuff that Sans says in the Last Corridor.
1) Given the rules of LV shown in the game, it would suggest that humans do give LV, because LV has to do with intent to kill - the more you kill, the more you distance yourself, the easier it is to harm, yada yada yada. The rules seem to show killing anything that seems to have value - for example, if you killed a plant you probably wouldn't get any LV - with an evil or malicious intent will gain LV.
2) Because this instance never happens in the game, it is unsure what would happen. Logistically, I would assume that the LVs from the other person would NOT carry over as LV is focused on intent to kill. I would assume that if you killed a random person, it would give you as much LV as killing a serial killer.
3) As I previously said, I do not believe that there is a link between LV and Determination, so I would also assume that monsters CAN gain LV. They may, however, call it something else, as (I think, correct me if I'm wrong) it is never shown in the game. (Except for Sans acknowledging its existence.)
Also for the other question:
No, human can not absorb a human soul it is stated in the signs in waterfall. There COULD be speculation that this is not correct, as the library and waterfall have given information that contradicts the prologue, but, assuming that they are correct, a human cannot absorb a human soul.
Sorry for any run-on sentences - I tend to have a problem with them!