Since there is no exact information on either the hunting method nor the size of the gathered bones, it wouldn’t be strange for small pray like rabbits to be taken home before disassembling.
That the hunting knife gives a bonus to hunting but bow don’t also support, that the hunting is based on traps and targets smaller pray.
And yes, I am aware that it might be simply a decision in the game design or a problem with the system.
As for the mana and live shards, I’m not sure, what they are (I might have missed or forgot an explanation). But since I found them after fight or in tressures, I assumed they are some kind of “organic” material forming inside of living creatures at some conditions.