Crossing borders in a rented car is no problem. I have never heard of rental company restricting it in western Europe. Actually crossing the border is no issue. Most cars get waved through, they only stop those that look suspicious.
What is a problem is renting a car in one country and handing in back in another, that will either cost a huge surcharge, or not be allowed. Returning the car in Germany will be no problem.
Some locations in the Jungfrau region are not accessible by car (Mürren, Wengen), you have to leave your car at the bottom of the valley.
There are no tolls on German Autobahn.
Driving on Autobahn/Autoroutes/Autostrada in Switzerland requires you to pay a toll. This is flat rate CHF 40 per year. You get a sticker called a "vignette" which you attach to the windscreen. If the car does not already have a Vignette for 2018, you will need to buy one at the border.
Autostrada in Italy have tolls, the usual system where you pay by distance.
P.S. Many towns in Italy have resident-only areas in the centre, called "ZTL". Make sure you learn the signs for these and obey them. They are enforced by automatic camera and fines come in the post a long time later.
P.P.S. Of course learn all road rules and signs for each country before venturing on the road.