Questionnaire with form or something else

Is it possible to create a questionnaire with Grav or with a plugin?

You could with some custom development, but I'd first check out if your needs could be met by using an existing survey tool and simply embed the form into Grav (this is what I would do myself).

Here is a video overview of embedding a simple Google Form (WordPress example shown🙂):
https://www.youtube.com/watch?v=timNmQTKC5Y

Lots more feature-rich services are also out there, many with a free plan option for 1 or 2 surveys. One of my favourite survey services is https://www.wufoo.com (https://help.wufoo.com/articles/en_US/kb/Embed).