As my mother's POA, do I still need that other document to speak to Medicare on my Mother's behalf?

When I contacted them about my cousin, I was told that I had to be appointed the Representative Payee through Social Security.

What address do I sent the POA and caregiver official papers to Medicare

If you have Durable POA then that gives to the right to speak on you parents behalf. You will have to submit a copy for there records. And depending on there procedure there might be a waiting period so POA documents can be reviewed. If you have just a simple question for medicare they should answer you directly without POA. I recently call medicare and inquiried about mom's Hospice I gave them moms info and introduced myself and they answered what I needed. However, If it is bill related or something more personal then they will probably want Durable POA proof. But they will tell you if they do or not. So give them a call make sure you have moms medicare card in front of you, her DOB, Soc. sec#. Like I said they might be able to help you based on questions asked w/o POA submitted.

@mrtvz64 - This is a great question that we get all the time in our call center. Thanks for asking. The short answer is that you need to have a Medical POA.
The Medical or health care power of attorney (POA) is a legal document that designates you — referred to as your mother's health care agent or proxy — to make medical decisions for her if she can't do that for herself.
These Medical POAs are different from a power of attorney that authorizes you to make financial transactions for your mom.
I hope that helps!
Ross