No this is not an option through US immigration law.

Yes you may do so at the oath ceremony.

No it should be the proper size. Request another proper version.

No this does not appear an option given information provided.

It can be transferred to any USCIS service center, which you cannot control.

More information is needed about your case.

Yes while possible in the US, may be a more viable option abroad.

Yes this is possible given his status as USC. Consult with an attorney for guidance.

Your return should be based on validity period of document.

Contact USCIS but this is likely not a mistake.