Normally the agent should be able to advise you of the annual fuel costs but it'll vary accordingly with your preferences, number of occupants compared to before etc.

It's a common system in rural parts and should work well, basically you have energy on tap and the tanks tend to be huge so you can buy lots of fuel. Maybe you need to work out the tank level on moving in, eg if the tanks are near-empty then budget CHF 1,000 just to get some in there to see you through winter

There's a fire risk but obviously the % of houses that burn down because of the fuel tank is minimal, you should have insurance anyway; in my canton it's compulsory. More realistically you can get functional problems, ideally get the landlord to agree to an annual service, basically to remove the soot from the burner, and clean the filter for the fuel coming into the burner. It's a quick job and in the owner's interest as servicing is cheap compared to the whole thing breaking down, fuel leaking etc etc