For a single webpage is it possible to add questions and answers complementing the webpage content. I am talking about non-visible (meta) content that will just help in SEO.
To answer your question, no it is not possible without violating Google's guidelines.
According to Google's structured data guidelines:
Don't mark up content that is not visible to readers of the page.
So adding extra FAQs to structured data, if they are not visible on the page, is a violation and is likely to get your structured data ignored.
I imagine that other search engines probably have similar policies.