yes you do. They tell you the category and then you have to make your choice.

On Jeopardy episodes for Oct 29 2007 and July 4 2008 Country Music was a Jeopardy Category and on July 19 2007 Country Music Stars on Film was a Category. There are also Country Music questions on some other dates. A link to a number of questions on country Music has been provided to allow you to see actual Jeopardy country music questions. You can also you the Jeopardy archive to search for others with the search bar at the top of any Jeopardy Season on the Archive.

If you are talking about someone in danger, it is "in jeopardy." If you are talking about the television show, it's "on Jeopardy."

Alex Trebek has jokingly referred to this situation (making a risky Final Jeopardy bet with a dominating lead) several times in the actual show as "pull[ing] a Cliff Clavin." see related link

There are 61 answers/questions in a complete game of Jeopardy - 30 in the Jeopardy Round, 30 in the Double Jeopardy Round and 1 in the Final Jeopardy Round.