I am developing an ESRI web app. As a part of this app, I need to make a widget, where users can answer a few predefined questions (5 or 6 questions) and then be able to print it or save it as pdf. Is there such an existing app? or we can build this app from a template?
No existing app / template I am aware of.
You can easily build a custom widget for your needs. You can lookup the print widget documentation here: https://doc.arcgis.com/en/web-appbuilder/create-apps/widget-print.htm
In the same link for print widget, on the left side bar menu you will find all you need to quickly build your widget requirements.
Also the below forum thread discussed in past about how to publish your widget for others to use