Do you know that we need to pay for the transit fee when going from Germany to Austria and Switzerland ?

Please indicate at the time of renting that the "border crossing fee" will be charged; when driving into Austria (Switzerland), purchase a high-speed ticket (day pass) before the border.

You don't need to pay for the border-crossing fee when going from Germany to Austria, but you need to buy the expressway ticket which can be bought at the gas station on the border. There are tickets for 7 days, 15 days and 1 month. This time we drove from Germany to Switzerland, and the car company has already charged us a border-crossing fee of 25 euros, so we didn't buy the expressway fee when we drove to Switzerland.

I drove from Munich to Zurich, Lucerne, Interlaken, and then back to Liechtenstein, Innsbruck, Salzburg, and finally back to Munich. There was only a 10€ tunnel fee before arriving in Innsbruck, Austria, and I didn't pay anything else.

You definitely need to buy highway toll tickets in Austria. You can buy them at rest stops or gas stations near the border. It's 9.5 euros for 10 days. I forget the German word for toll, but it's something like VIT***. If you're still not sure, ask the hotel staff to help you find a small town or village near the German border. Then use Google Maps to find a gas station in that area.

Sure, you can buy it at rest stops on the Autobahn in Germany.