Is there a way to export topics/posts that are displayed when filtering?

Stick .json on the end of the path and that will give you a JSON export?

e.g. https://mydiscourse.org/tag/my-fab-tag/l/top.json?period=quarterly

or https://mydiscourse.org/search.json?q=user%3A%20bob%20cats

Then just copy the text from the browser … and store wherever.