I am using Mobility as a practice vehicle for my Driving test to convert the license.
I have signed up 40 chf third party insurance, this cover upto a limit to 2500chf.

Since I am paranoid and would like to opt for an insurance that would save me incase of any accident,any suggestions?

Contact your current general home insurer; all will cover car insurance. If you don't know where to turn, perhaps contact Jenny, a Member who has provided great advice for thousands of people. She's an independent and will know what's what.

Good luck with the test.

For another 125 chf per year, Mobility reduces the excess much much further. We have this check www.mobility.ch under .the faq perhaps

You have wasted 40 bucks, this insurance covers only costs for occasional but not repeatly driving the same borowed car or a car from the same owner, it would be less than 10 times a year. Mobility cars are covered anyway by their insurance.
I doubt you can get any additional insurance to cover excess and further covarage like passenger in a car which is not regitered on your name. Read the terms of contract from mobility and their insurance terms.

You are saying you would use mobility cars to practice driving, make sure that is alowed by mobility and the set of regulations regarding to your actual driving license while beeing a permanent resident.