Is it possible to know what search terms have been used to find a jr site?
Using Jamroom
In the jr_jrsearch_fulltext table the search terms used ON your site are stored but only something like GoogleAnalytics will be able to tell you what search terms were used to get the users TO your site.
There are many analytics packages but GA is popular because its free.
Search "Google Analytics Alternatives" for options, eg:
https://plausible.io/blog/google-analytics-alternatives