What’s the best way to ask for user feedback about a specific element/section in a website?

I'm working a feedback form for a clinical platform which is used by health care providers (mainly doctors). The website has a patient dashboard where the doctor can see the patients clinical record like his test scores and more.

Now, we would like to ask for user feedback (mainly from doctors) on a specific patient detail on the website to understand how much the info shown is in alignment with their clinical judgment.

Here's what I have created: enter image description here

A few points that bother me are:

  • I feel it's not good to have general feedback form since here we need feedback on specific info shown in the page
  • The response from the user to this is critical since it is about a clinical score. Still, need the option to ignore/hide the feedback prompt forever in that page
  • The feedback prompt/form should not hinder other regular actions of the user in the website
  • To get more precise feedback it's necessary to rate the experience in a scale from 1 to 5
  • Will using emoji's to rate something avoid confusion and be more clear?
  • Due to limited space in the section, I used a simple Yes/No question within the section and on choosing a response he would be presented with a popup with a detailed form (both Yes and No options)