It's technically possible, but the "+ Legg til fler/+Add More/" part of the dynamic form you linked isn't very easy to replicate.
First the good news: dynamically changing input or hidden field values based on sliders, radio buttons, and so on is relatively easy with some JavaScript injection code to manipulate the DOM, the tricky part is dynamically adding new fields.
When you create a form block, Squarespace registers its parameters with the backend, and will only recognize the set amount of input fields you used to build it on submit. You can use JavaScript to dynamically add fields to the form in the DOM, but Squarespace won't recognize them, and will submit the form without passing their values.
HOWEVER, you should be able to create a hidden form field in the Squarespace form builder, use JavaScript to dynamically add/remove input fields, then set the newly created fields to concat their values and dynamically change the hidden field. It's not super elegant, and requires a good amount of custom JavaScript code, but it should be technically possible. Unfortunately, there is no out-of-the-box form builder solution that will work with Squarespace forms, so making this work will require you getting your hands dirty with JavaScript.
Hope that helps.