You could update the parent informally for little things but the bigger things that need to be documented should take place in a formal meeting with all parties present. If you feel uncomfortable you could always reach out to your supervisor to set up the meeting for you.

Although this student is a child of an administrator this child needs to be treated just as another other child would in your classroom. The administrator should understand that they need to go through the same channels as other parents to address issues with their children. Before or afters school meet with the administrator to set up a parent teacher conference to discuss the issues that are being seen in the classroom. If you feel uneasy about it maybe have another administrator present with you when you speak to them about setting up a conference.

As an administrator they should understand that this would be strictly professional and know that you would just be doing your job. There shouldn't be a problem as a teacher doing your job.

I know how you feel in this situation, I am also in a school where there are many faculty children. I have noticed that the best way to deal with behavior issues is to address them right away. Trying to put it off or give them more chances because they are an administrators child will just cause more problems in the end. If it is a serious problem it should definitely be documented and both parents should be present for any type of conference.

All students including administrators children should be treated equally and fairly.

You could apply theories and practices that was implemented in the classroom, in the mean time try to reach out to the parent for the documentation.

Stay consistent with how you communicate with other parents, but try to have professional conversations in the right settings.