This is not possible with Airtable’s forms. You would need to use external form apps to do this.
However, note that even with external apps, your users can’t add/remove fields… they can only add/remove new rows (aka “line items” or “linked records” or “lists”) in your forms.
There are only 3 form apps that I know of that support this feature:
1. Fillout, which natively communicates with Airtable in real time, and gives tons of advanced features that are all Airtable-specific.
2. JotForm is possibly the most feature-rich form software on the Internet. After your forms are submitted in JotForm, you would use Make’s JotForm integrations to send the data to Airtable.
3. Cognito Forms is another fantastic form software. And you can send data from Cognito Forms to Airtable using Make’s Cognito Forms integrations.
There is a small learning curve with Make, which is why I created this basic navigation video to help. I also provide the links to a few other Make training resources there as well.
p.s. If you have a budget for your project and you’d like to hire an expert Airtable consultant to help you with any of this, please feel free to contact me through my website: Airtable consulting — ScottWorld