Multiple Parent Category URLs

You shouldn’t need to do any of that.

When you set up a category in the backend of a WordPress website, the archive is normally created/taken care of for you. So if you create a category called ‘Massive Dogs’ and you got to “/massive-dogs’ after you have created a post in that category (and the slug is the same), you should see your post item.

The URL would only reflect that if you had parent/child categories.

http://www.wpbeginner.com/beginners-guide/how-to-add-categories-and-subcategories-to-wordpress/

Anything beyond that would likely need you to create some custom functionality in the function file and/or create some custom templates.

It would be interesting to know why you would need that kind of URL structure. Surely anything in 'topic1/news' would just be news?

I hope this helps but if not, comment and I’ll be happy to help further 🙂