I want to display SharePoint survey questions on Home page or web part. I'm using publishing pages instead of site pages.
But I need to display the question on the page.
You can achieve that using SharePoint Designer.
But, the publishing page cannot be edited directly using SharePoint Designer.
You need to create a page layout and insert New Item Form to it using SharePoint Designer. Design the form such as width as you want. Create a Home page with the new page layout.
If this is for a single site/survey and a small number of questions, the fastest thing may be to recreate the questions in a rich text editor/content editor web part and manually link to the new form view so the user can provide their answer once they click on the link. If they have already answered and you have the survey set to one reply per user, then they will get the message that they have already submitted a response.
Otherwise you will need to create a custom app to directly show the survey questions to users.
Here are some resources that can help you research how to do this: