What does it mean if a creature (Niv Mizzet, Parun) has a passive ability that says this "this spell can't be countered"? Is that only when casting the spell or it can't be countered (unsummon, murder, bake into pie etc) at all?
A card is identified as a spell only when it is on the stack. Therefore, while it is on the stack, your opponent can't use anything like Counterspell on Niv-Mizzet, Parun
Once the spell leaves the stack it is no longer a spell. If it makes it to the battlefield then it is a creature and is subject to cards like Murder. Note that cards like Murder and Unsummon are usually not considered counters but removal. You counter a spell while it is on the stack but you remove a permanent from the battlefield.
Contrast this with a card like Humongulus which can be countered while it is on the stack but cannot be the target of Murder once it is on the battlefield as a creature.
Neither ability prevents your opponent from targeting the card in the graveyard or in your hand.
Once the spell leaves the stack it is no longer a spell. If it makes it to the battlefield then it is a creature and is subject to cards like Murder. Note that cards like Murder and Unsummon are usually not considered counters but removal. You counter a spell while it is on the stack but you remove a permanent from the battlefield.
Contrast this with a card like Humongulus which can be countered while it is on the stack but cannot be the target of Murder once it is on the battlefield as a creature.
Neither ability prevents your opponent from targeting the card in the graveyard or in your hand.