Tax implication questions are best addressed with your tax certified accountant. Bankers are not licensed to provide tax advice.

Unofficially, first and foremost the IRS wants their cut. If your dad is listed first, does he want to assume the tax liability? Often the bank will report the interest income on the first SSN listed.

How can a name be taken off of a CD if My name is the seconary person on it or benificiary? Wouldn't I need to sign to give permission to take it off or to change it? Doe only the primary have the authority to do so?

Unless a joint CD is specifically opened requiring two signatures, either owner has the right to close the CD and withdrawal the funds as any time without the signature of another party.
If you are a beneficiary of a CD, your have no legal right to the funds until the owner(s) die. The owners have the right to change beneficiaries at any time without the beneficiaries knowledge or consent.

If my Father is sick and has dementia and the power of attorney is a sibling, Why does she (sibling) have the right to change all financial cd's in her name? He was not sick when he originally had the cd's put in my name and my Father's names. She had them changed after he got dementia. Why can I do?

In most states, and attorney-in-fact does not have the right to change ownership of accounts, unless the POA document specifically grants them the right to gift funds to themself. I cannot offer an opinion on whether or not the sibling or the bank acted properly. Citing privacy laws, the bank will most likely not give you access to these documents. You will need the services of an attorney unless you are representing yourself, and will have to subpoena the bank for any records regarding these transactions. If the sibling was able to change the ownership without being granted the authority to do so, you could possibly have a case for breach of fiduciary duty against her or the bank. However, if your father drew up the POA and gave the sibling the right to reallocate funds in the document, and she excercised that power, then you have no legal claim to the funds.

The unknown is what was your capacity? As Crowman noted if you were a beneficiary you had no ownership and this POA may have well allowed that change. Ownership would be a separate issue. If you feel this person is abusing an authority you need to consult an attorney to determine what your rights are.