There are absolutely accommodations that can be made for parents who don't want certain aspects of the students data to enter the G Suite system. But you have to participate and engage with your district, and not just let the wheels of bureaucracy turn for new student enrollment.
I'd be very curious what you mean here. I can definitely understand the possibility of being entered in under another name or the like, to try and avoid traditional PII, but students are supposed to complete and submit work through Google Classroom as well. Particularly in light of Google's AI work, things like an essay a student submitted is, at the very least, personal data, but very possibly, personally identifiable information. There is no realistic anonymity from just hiding someone's name.
I have significant doubts the school district is going to be particularly tolerant of "grade all students on Google Classrom, but this student needs to be graded by hand and recorded on paper" requests.
