How to limit each response to one per person while keeping responses anonymous?

Yes. The way to do this is to enable the Duplicate Submission Check with the IP address mechanism, and simply don't add any identifying field (name, email, login) to your form.
Go to the Settings tab, open the General section, enable Duplicate Check, and choose 'Duplicate check based on users IP Address'. FormNX then blocks a second submission from the same IP without ever asking who the respondent is - so each person can answer only once and the responses stay anonymous. You can set a custom error message that shows when a repeat submission is detected.
One thing to keep in mind: people on the same shared network (an office, school, or household behind one router) often share a single public IP, so the IP method may treat them as the same person. If that's a concern for your audience, the trade-off is to use the input-field mechanism (e.g. email) instead - but that requires collecting an identifier and is no longer fully anonymous.
For full setup steps see the documentation: https://formnx.com/details/docs/features/submis...