Is it possible to add fields to a Google Form which are visible only to specific users (based on their email ID)? Or allow only users whose email IDs fall in a set to fill the fields?
Google Forms doesn't include a feature to hide questions.
Google Forms could use page navigation to control wich questions will be available for the respondents but it's controlled by multiple choice questions, not by users ID.
Create an specific form for each set of users then send to each of them the corresponding form.
You can select a range of cells, then go to Tools > Protect Sheet...
Review settings, hit "Set permissions", Select "Custom..." and add the email addresses of the people who you'd like to have access.
It'll make the said sheet/range of cells non-editable for everybody else, still not hidden though.