I did it mainly with custom code using val(). and some if statements in jQuery.
You do not need to use multiple form blocks. You just have to put all your fields in sections (divs) just as you have done but inside one form element. Then the next button on each section can link to the next but all inside the form.
As for the checkboxes, here you need custom code. This time, DO NOT DELETE the checkbox field. We will be styling the checkbox element itself and reducing the opacity of the checkbox-field so that it is invisible but still present. Here is an example I just made for you. Pay attention to the structure and the active hidden active class on the topmost element.
Clonable: https://preview.webflow.com/preview/clickart-sandbox?preview=811e1b25b800f0a0037deb5a69d7efa5 (look for the page with your username)
Then just a small jQuery click function;
EDIT: I just realized you can do this without custom code. You will need to add a div (bg-color) inside the checkbox element. use z-index to bring the checkbox field to front, above all other elements. the apply a click interaction to show the bg-color div on first click and hide it on second click. Long method but native.
The you will apply an click interaction