Does the power of attorney have to be signed by an attorney?

In the presence of a Notary Public, preferably with witnesses.

No. The testator must sign their own will. The attorney in fact is not needed.

No, a power of attorney can never be applied to a will.

A power of attorney is a written instrument. You can purchase a fill in the blank form or have an attorney prepare a power of attorney for you.

Some states do require the attorney-in-fact to also sign the form.