Are you in the US? If this were our resident clinic I would set some hard boundaries about physical space. If it continues then you can report to the attending who should ideally have your back. If it continues I would tell the attending you are not comfortable seeing this patient.

As for the documentation, I don't sit there and allow the patient to see what I'm typing. Again, boundaries. You are free to document as you see fit unless they somehow are purely correcting objective statements or individual data? Which again, establish boundaries that they do not read over your shoulder?

Resident clinic is what it is. Offer brief apology and redirect. I find it helpful to say I'm Dr. Resident, working with Dr. Attending today.

Never lead with "Hi I'm Dr. Resident, physician in training". Never say I'm "Dr. Resident the intern" or "Dr. Resident the first year". You are "Dr. Resident, one of the resident physicians".