Have you looked on comparis.ch? You can set your search parameters for single family houses only. There are very few of them available to rent, but when we were looking (in the past month or two) we did see a few for rent, so they are out there. But my guess is you will end up having to compromise on something that you want, just because the supply is so limited, the chances of getting something that will tick all your boxes will be smaller than in another country (in my opinion).

edited to add: to answer your other question, I think renting houses is very rare. Most houses seem to be owned/owner-occupied from what I understand.