Flat tires are certainly the most likely mechanical problem you might face. Therefore, most cyclists always carry a spare tube, tire levers and a pump so that they can fix the problem and keep riding if this happens. Obviously, you don't want to have to replace a tube for the first time ever when you're on the side of the road. Therefore, I suggest practicing at home a few times first and then you'll feel comfortable doing it when the need arises and you won't have to be so worried about it happening.

As for tips on how to change a tube successfully, just use Google to search for something like "fixing a flat bicycle tire" or "changing a bicycle tube" and you'll find lots of info.

Other problems that you might have are much rarer and much more varied, so I wouldn't worry about them for now. You can wait until another rider comes along and ask him/her for help, or head to the nearest train station like you did. I always make sure when I go out that I have enough money to get me and my bike back home on the train from however far I might get during that ride. If you're on a road in Switzerland then it is pretty rare that you get more than 5km away from the nearest train station, which is just a one hour walk if you have to do it.

I wouldn't worry too much about Swiss drivers, I find that they are generally pretty good when it comes to cyclists. To reduce your fears of them, I find it helps to have a rear-view mirror on the bike. If you have a mountain bike, you can get one designed to fit into the end of your handlebars that works quite well.

I hope you enjoy lots more stress-free riding in this beautiful country.