In other words, there won't be this problem if we don't take the expressway? Is the toll collected at the checkpoint when crossing the border? Can we buy the expressway toll at the same time? Because I don't know when the last gas station in Switzerland is, I'm afraid I'll accidentally enter the Swiss expressway ?

If you have already told the car agency and paid the fee, then it doesn't matter. The highway fee must be paid if you drive on the expressway. Google navigation to the gas station closest to Switzerland to buy. These are two fees. When we crossed the border from France to Switzerland, we encountered both French and Swiss police checking cars, but they didn't check small cars.