Can the party given healthcare POA decide where the elder will live without asking their siblings?

Yes.. but I know from experience that when siblings are not consulted, there can be great conflict.

Yup!!!

Yes, Healthcare POA can decide this as long as the elder agrees. If the elder isn't mentally sound, it's up to the Healthcare POA as long as the elderly family member can afford it. If the Healthcare POA are unsure, the Healthcare POA should check with whoever has the Financial POA. But unless the siblings will create problems, I suggest the Healthcare POA talk to them first anyway in hopes that all can agree even though the Healthcare POA will have final say-so. Good luck!!