Is an accreditation body a government body?

1. Is an accredited body a government body?

In accordance with SAC, the accreditation is (you can see this definition in the FAQ page https://www.sac-accreditation.gov.sg/resources/faq:
Accreditation is the endorsement by an authoritative body (such as SAC) of an organisation's competence, credibility, independence and integrity in carrying out its conformity assessment activities, such as testing, calibration, inspection and certification.
So, an accreditation body needs to be independent, so usually is a body related to the govern of each country.

2. From my understanding, an accredited body is the body that certifies organisation. (This is my company’s goal, to become an accredited body). Thus, in order to become an accredited body, does my company needs to be certify the ISO/IEC 27001 requirements first?

If you want to certifies companies, you need to be a certification body, and you need to be accredited by the accreditation body of your country (SAC). For more information to obtain the accreditation, you can also see the FAQ page of SAC, please read What is the general procedure for getting accreditation? : https://www.sac-accreditation.gov.sg/resources/faq. And in this case I think that it is not necessary that your company certify the ISO 27001, but you need to implement the ISO 17021 and ISO 27006.