Can a sibling with POA share POA responsibilities with another sibling before parent's actual death?

Being POA does not mean you have to be the Caregiver or fetch and carry.

A PoA can't confer legal authority to act on parent's behalf (like signing checks, managing affairs directly, completing transactions per the document) but can do other things that the PoA asks them to do. The Executor takes over the minute a person passes away and the PoA authority ends.

POA ends with death.

Yes, a POA can delegate responsibility to others, they just have to ensure that every action is in accordance with the statutes of the state that governs the POA.

What kind of duties are you asking about? Obviously the other sib won't have the authority to sign legal documents, but there is a lot of other things they can do at the direction of the POA or just as any helpful family member or friend would.