How to competently implement a unique quiz/questionnaire?

Question

JavaScript

Toasters, hello! (:
There is a task to make a 2-8 step questionnaire for collecting leads. The market offers many constructors for assembly, but they have one problem - the inability to make a unique design. The developers of popular constructors themselves do not provide such a service.
The functionality of the required questionnaire is as follows:
1. Logic branching depending on the selected answers
2. Default controls: sliders, lists, date pickers, radio buttons, checkboxes, etc. Like Marquiz for example
3. Ability for us to change/edit/delete questions and edit text with graphics, logic
4. Mixed result page type: it should display the cost depending on the selected answers
Questions arise:
1) If, for example, you find a layout designer and give him ready-made layouts, what CMS is suitable for such a quiz? Do you need a CMS at all? Can it be easier to transfer the resulting edits directly to the layout designer?
2) Are there designers who provide the service of layout and assembly of quizzes with their own functionality, but with the client's design?
3) Do I understand correctly that for such a lead collector: mail, phone numbers, etc., a backend is required?
4) What technologies are suitable for such a "own" designer? Maybe there are some ready-made solutions that you can finish for yourself? Alya some WordPress plugin where you can use its functionality but with a completely unique design, etc.
Or maybe in general you can take and copy the functionality, and then just use it on your design? But it's hard to believe that you can find ready-made scripts.
I would be grateful for any useful information, advice and personal experience.