Different way for users to add content on pages On my website each user can only edit the existing main content via the 'edit' button on the page.

I don't want each user to see what was added previously on the page like it happens on my website: 

Is there a way the user can add their own new content and be displayed on the page in ascending order (new content on top of the previous one) WITHOUT modifying/ viewing the previous post? E.g. like on this example I found online:
Yes. You can use the built in content types and the default 'node' page which allows this for just the front page or if you want more complex uses with multiple pages you will need something like views and a custom content type with a taxonomy term to tie the content pages to the view.