How can I add a survey question on a SharePoint 2013 page as shown in the image below?
If it’s for single page, you could add html to Content Editor web part and trigger client function and then insert data to custom list by JSOM. For CRUD by JSOM, you could check below thread for reference. https://msdn.microsoft.com/en-us/library/office/hh185011(v=office.14).aspx
If you need add this to multiple page, you have to consider to add the code to page layout/master page.