Hey Diana
In S&F free, S&F simply uses URLs that should work in WP regardless of S&F’s existence.
For example, when you search for a category you will be redirected to www.yoursite.com/category/some-category-name
This is a URL already existing for your archives.
Then when you use a search term, S&F just adds a ?s=searchterm
to your URL – again this should work in WP as standard.
So a search for both a category and a search term should result in a URL like:
www.yoursite.com/category/some-category-name/?s=searchterm
If this is the kind of URL you get, but the results are not accurate, then there is an issue somewhere else in your setup, possibly your theme, plugin or custom code.
I would probably try disabling plugins and testing on a WP theme to see if you still get the issue.
Thanks