If you're never alerted about malware you might at some point start thinking if your anti-virus(AV) really works. With the EICAR files you can easily test this. They are safe and harmless files but are detected by AV products as if they were a virus. I think it's a good thing to test this so you know how the F-Secure message looks like when it detects a virus, and of course also verify that the virus detection works as it should: https://www.f-secure.com/v-descs/eicar.shtml
These files should be blocked during download (but note that regarding zip files and "real time" scan, files inside archives aren't scanned until they are executed or extracted)
To test the Browsing Protection(part of Internet Security - Online Safety) in your browser(s), go to this site: http://unsafe.fstestdomain.com/ If it's working you should see an F-Secure message like this one:
It's 6 tests, all trying to launch executable files that are safe and harmless files but detected as malicious. If the protection is working, all files should be blocked and NOT launched/opened. Depending on what browser you use, some of the tests will show a successful block as a message like "The website declined to show this webpage" or "HTTP 403 Forbidden". If you are able to actually open or download any of the files, it means the test failed.
F-Secure Safe Search
If you don't have Browsing Protection(or even if you do) I recommend F-Secure Safe Search as your search engine. It's a Google powered search with F-Secure safety ratings for the search results: https://search.f-secure.com/