Section 17 of the Registration Act, 1908, is silent about registration of a power of attorney for an immovable property. You may have to examine the relevant amendments, if any, made in the State laws to the above Act. For example, in Maharashtra, there is an amendment to S. 17 of the Registration Act, 1908, as per which an irrevocable Power Attorney relating to transfer of immovable property shall be compulsorily registered. So, please check in your state if there is any such amendment.
Notarized POA generally refers to POA affirmed before a Notary and it may or may not be registered. Registered POA, on the other hand, would be registered before the Sub-Registrar in accordance with legal provisions, such as the Registration Act.
Notarized POA should be usable in court, if the registration thereof is not compulsory.
Answer to your other questions may depend on the terms of the POA and/or the law applicable to your state.
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